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Título : Functional Analysis, Calculus of Variations and Optimal Control Tipo de documento: documento electrónico Autores: Clarke, Francis ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 264 Número de páginas: XIV, 591 p. 24 illus., 8 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4471-4820-3 Idioma : Inglés (eng) Palabras clave: Mathematics Functional analysis System theory Calculus of variations Mathematical optimization Analysis Variations and Optimal Control; Optimization Continuous Systems Theory, Control Clasificación: 51 Matemáticas Resumen: Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields Nota de contenido: Normed Spaces -- Convex sets and functions -- Weak topologies -- Convex analysis -- Banach spaces -- Lebesgue spaces -- Hilbert spaces -- Additional exercises for Part I -- Optimization and multipliers -- Generalized gradients -- Proximal analysis -- Invariance and monotonicity -- Additional exercises for Part II -- The classical theory -- Nonsmooth extremals -- Absolutely continuous solutions -- The multiplier rule -- Nonsmooth Lagrangians -- Hamilton-Jacobi methods -- Additional exercises for Part III -- Multiple integrals -- Necessary conditions -- Existence and regularity -- Inductive methods -- Differential inclusions -- Additional exercises for Part IV En línea: http://dx.doi.org/10.1007/978-1-4471-4820-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32194 Functional Analysis, Calculus of Variations and Optimal Control [documento electrónico] / Clarke, Francis ; SpringerLink (Online service) . - London : Springer London : Imprint: Springer, 2013 . - XIV, 591 p. 24 illus., 8 illus. in color : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 264) .
ISBN : 978-1-4471-4820-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Functional analysis System theory Calculus of variations Mathematical optimization Analysis Variations and Optimal Control; Optimization Continuous Systems Theory, Control Clasificación: 51 Matemáticas Resumen: Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields Nota de contenido: Normed Spaces -- Convex sets and functions -- Weak topologies -- Convex analysis -- Banach spaces -- Lebesgue spaces -- Hilbert spaces -- Additional exercises for Part I -- Optimization and multipliers -- Generalized gradients -- Proximal analysis -- Invariance and monotonicity -- Additional exercises for Part II -- The classical theory -- Nonsmooth extremals -- Absolutely continuous solutions -- The multiplier rule -- Nonsmooth Lagrangians -- Hamilton-Jacobi methods -- Additional exercises for Part III -- Multiple integrals -- Necessary conditions -- Existence and regularity -- Inductive methods -- Differential inclusions -- Additional exercises for Part IV En línea: http://dx.doi.org/10.1007/978-1-4471-4820-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32194 Ejemplares
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Título : Functional Equations and Inequalities with Applications Tipo de documento: documento electrónico Autores: Kannappan, Palaniappan ; SpringerLink (Online service) Editorial: Boston, MA : Springer US Fecha de publicación: 2009 Colección: Springer Monographs in Mathematics, ISSN 1439-7382 Número de páginas: XXIV, 816 p. 16 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-89492-8 Idioma : Inglés (eng) Palabras clave: Mathematics Difference equations Functional analysis Applied mathematics Engineering and Equations Analysis Applications of Clasificación: 51 Matemáticas Resumen: Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. Nowadays, the field of functional equations is an ever-growing branch of mathematics with far-reaching applications; it is increasingly used to investigate problems in mathematical analysis, combinatorics, biology, information theory, statistics, physics, the behavioral sciences, and engineering. This self-contained monograph explores all aspects of functional equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, and many other basic tools in analysis. Each chapter examines a particular family of equations and gives an in-depth study of its applications as well as examples and exercises to support the material. The book is intended as a reference tool for any student, professional (researcher), or mathematician studying in a field where functional equations can be applied. It can also be used as a primary text in a classroom setting or for self-study. Finally, it could be an inspiring entrée into an active area of mathematical exploration for engineers and other scientists who would benefit from this careful, rigorous exposition Nota de contenido: Basic Equations: Cauchy and Pexider Equations -- Matrix Equations -- Trigonometric Functional Equations -- Quadratic Functional Equations -- Characterization of Inner Product Spaces -- Stability -- Characterization of Polynomials -- Nondifferentiable Functions -- Characterization of Groups, Loops, and Closure Conditions -- Functional Equations from Information Theory -- Abel Equations and Generalizations -- Regularity Conditions—Christensen Measurability -- Difference Equations -- Characterization of Special Functions -- Miscellaneous Equations -- General Inequalities -- Applications En línea: http://dx.doi.org/10.1007/978-0-387-89492-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33918 Functional Equations and Inequalities with Applications [documento electrónico] / Kannappan, Palaniappan ; SpringerLink (Online service) . - Boston, MA : Springer US, 2009 . - XXIV, 816 p. 16 illus : online resource. - (Springer Monographs in Mathematics, ISSN 1439-7382) .
ISBN : 978-0-387-89492-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Difference equations Functional analysis Applied mathematics Engineering and Equations Analysis Applications of Clasificación: 51 Matemáticas Resumen: Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. Nowadays, the field of functional equations is an ever-growing branch of mathematics with far-reaching applications; it is increasingly used to investigate problems in mathematical analysis, combinatorics, biology, information theory, statistics, physics, the behavioral sciences, and engineering. This self-contained monograph explores all aspects of functional equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, and many other basic tools in analysis. Each chapter examines a particular family of equations and gives an in-depth study of its applications as well as examples and exercises to support the material. The book is intended as a reference tool for any student, professional (researcher), or mathematician studying in a field where functional equations can be applied. It can also be used as a primary text in a classroom setting or for self-study. Finally, it could be an inspiring entrée into an active area of mathematical exploration for engineers and other scientists who would benefit from this careful, rigorous exposition Nota de contenido: Basic Equations: Cauchy and Pexider Equations -- Matrix Equations -- Trigonometric Functional Equations -- Quadratic Functional Equations -- Characterization of Inner Product Spaces -- Stability -- Characterization of Polynomials -- Nondifferentiable Functions -- Characterization of Groups, Loops, and Closure Conditions -- Functional Equations from Information Theory -- Abel Equations and Generalizations -- Regularity Conditions—Christensen Measurability -- Difference Equations -- Characterization of Special Functions -- Miscellaneous Equations -- General Inequalities -- Applications En línea: http://dx.doi.org/10.1007/978-0-387-89492-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33918 Ejemplares
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Título : Functional Equations in Mathematical Analysis Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Rassias, Themistocles M ; Brzdek, Janusz Editorial: New York, NY : Springer New York Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Springer Optimization and Its Applications, ISSN 1931-6828 num. 52 Número de páginas: XVII, 749 p. 6 illus., 1 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4614-0055-4 Idioma : Inglés (eng) Palabras clave: Mathematics Difference equations Functional analysis Special functions and Equations Analysis Functions Clasificación: 51 Matemáticas Resumen: Functional Equations in Mathematical Analysis, dedicated to S.M. Ulam in honor of his 100th birthday, focuses on various important areas of research in mathematical analysis and related subjects, providing an insight into the study of numerous nonlinear problems. Among other topics, it supplies the most recent results on the solutions to the Ulam stability problem. The original stability problem was posed by S.M. Ulam in 1940 and concerned approximate homomorphisms. The pursuit of solutions to this problem, but also to its generalizations and/or modifications for various classes of equations and inequalities, is an expanding area of research, and has led to the development of what is now called the Hyers–Ulam stability theory. Comprised of contributions from eminent scientists and experts from the international mathematical community, the volume presents several important types of functional equations and inequalities and their applications in mathematical analysis, geometry, physics, and applied mathematics. It is intended for researchers and students in mathematics, physics, and other computational and applied sciences Nota de contenido: Preface -- 1. Stability properties of some functional equations (R. Badora) -- 2. Note on superstability of Mikusinski’s functional equation (B. Batko) -- 3. A general fixed point method for the stability of Cauchy functional equation (L. Cadariu, V. Radu) -- 4. Orthogonality preserving property and its Ulam stability (J. Chmielinski) -- 5. On the Hyers-Ulam stability of functional equations with respect to bounded distributions (J.-U. Chung) -- 6. Stability of multi-Jensen mappings in non-Archimedean normed spaces (K. Cieplinski) -- 7. On stability of the equation of homogeneous functions on topological spaces (S. Czerwik) -- 8. Hyers-Ulam stability of the quadratic functional equation (E. Elhoucien, M. Youssef, T. M. Rassias) -- 9. Intuitionistic fuzzy approximately additive mappings (M. Eshaghi-Gordji, H. Khodaei, H. Baghani, M. Ramezani) -- 10. Stability of the pexiderized Cauchy functional equation in non-Archimedean spaces (G. Z. Eskandani, P. Gavruta) -- 11. Generalized Hyers-Ulam stability for general quadratic functional equation in quasi-Banach spaces (J. Gao) -- 12. Ulam stability problem for frames (L. Gavruta, P. Gavruta) -- 13. Generalized Hyers-Ulam stability of a quadratic functional equation (K.-W. Jun, H-M. Kim, J. Son) -- 14. On the Hyers-Ulam-Rassias stability of the bi-Pexider functional equation (K.-W. Jun, Y.-H. Lee) -- 15. Approximately midconvex functions (K. Misztal, J. Tabor, J. Tabor) -- 16. The Hyers-Ulam and Ger type stabilities of the first order linear differential equations (T. Miura, G. Hirasawa) -- 17. On the Butler-Rassias functional equation and its generalized Hyers-Ulam stability (T. Miura, G. Hirasawa, T. Hayata) -- 18. A note on the stability of an integral equation (T. Miura, G. Hirasawa, S.-E. Takahasi, T. Hayata) -- 19. On the stability of polynomial equations (A. Najati, T. M. Rassias) -- 20. Isomorphisms and derivations in proper JCQ*-triples (C. Park, M. Eshaghi-Gordji) -- 21. Fuzzy stability of an additive-quartic functional equation: a fixed point approach (C. Park, T.M. Rassias) -- 22. Selections of set-valued maps satisfying functional inclusions on square-symmetric grupoids (D. Popa) -- 23. On stability of isometries in Banach spaces (V.Y. Protasov) -- 24. Ulam stability of the operatorial equations (I.A. Rus) -- 25. Stability of the quadratic-cubic functional equation in quasi-Banach spaces (Z. Wang, W. Zhang) -- 26. u-trigonometric functional equations and Hyers-Ulam stability problem in hypergroups (D. Zeglami, S. Kabbaj, A. Charifi, A. Roukbi) -- 27. On multivariate Ostrowski type inequalities (Z Changjian, W.-S. Cheung) -- 28. Ternary semigroups and ternary algebras (A. Chronowski) -- 29. Popoviciu type functional equations on groups (M. Chudziak) -- 30. Norm and numerical radius inequalities for two linear operators in Hillbert spaces: a survey of recent results (S.S. Dragomir) -- 31. Cauchy’s functional equation and nowhere continuous/everywhere dense Costas bijections in Euclidean spaces (K. Drakakis) -- 32. On solutions of some generalizations of the Golab-Schinzel equation (E. Jablonska) -- 33. One-parameter groups of formal power series of one indeterminate (W. Jablonski) -- 34. On some problems concerning a sum type operator (H.H. Kairies) -- 35. Priors on the space of unimodal probability measures (G. Kouvaras, G. Kokolakis) -- 36. Generalized weighted arithmetic means (J. Matkowski) -- 37. On means which are quasi-arithmetic and of the Beckenbach-Gini type (J. Matkowski) -- 38. Scalar Riemann-Hillbert problem for multiply connected domains (V.V. Mityushev) -- 39. Hodge theory for Riemannian solenoids (V. Muñoz, R.P. Marco) -- 40. On solutions of a generalization of the Golab-Schinzel functional equation (A. Murenko) -- 41. On functional equation containing an indexed family of unknown mappings (P. Nath, D.K. Singh) -- 42. Two-step iterative method for nonconvex bifunction variational inequalities (M.A. Noor, K.I. Noor, E. Al-Said) -- 43. On a Sincov type functional equation (P. K. Sahoo) -- 44. Invariance in some families of means (G. Toader, I. Costin, S. Toader) -- 45. On a Hillbert-type integral inequality (B. Yang) -- 46. An extension of Hardy-Hillbert’s inequality (B. Yang) -- 47. A relation to Hillbert’s integral inequality and a basic Hillbert-type inequality (B. Yang, T.M. Rassias) En línea: http://dx.doi.org/10.1007/978-1-4614-0055-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32732 Functional Equations in Mathematical Analysis [documento electrónico] / SpringerLink (Online service) ; Rassias, Themistocles M ; Brzdek, Janusz . - New York, NY : Springer New York : Imprint: Springer, 2012 . - XVII, 749 p. 6 illus., 1 illus. in color : online resource. - (Springer Optimization and Its Applications, ISSN 1931-6828; 52) .
ISBN : 978-1-4614-0055-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Difference equations Functional analysis Special functions and Equations Analysis Functions Clasificación: 51 Matemáticas Resumen: Functional Equations in Mathematical Analysis, dedicated to S.M. Ulam in honor of his 100th birthday, focuses on various important areas of research in mathematical analysis and related subjects, providing an insight into the study of numerous nonlinear problems. Among other topics, it supplies the most recent results on the solutions to the Ulam stability problem. The original stability problem was posed by S.M. Ulam in 1940 and concerned approximate homomorphisms. The pursuit of solutions to this problem, but also to its generalizations and/or modifications for various classes of equations and inequalities, is an expanding area of research, and has led to the development of what is now called the Hyers–Ulam stability theory. Comprised of contributions from eminent scientists and experts from the international mathematical community, the volume presents several important types of functional equations and inequalities and their applications in mathematical analysis, geometry, physics, and applied mathematics. It is intended for researchers and students in mathematics, physics, and other computational and applied sciences Nota de contenido: Preface -- 1. Stability properties of some functional equations (R. Badora) -- 2. Note on superstability of Mikusinski’s functional equation (B. Batko) -- 3. A general fixed point method for the stability of Cauchy functional equation (L. Cadariu, V. Radu) -- 4. Orthogonality preserving property and its Ulam stability (J. Chmielinski) -- 5. On the Hyers-Ulam stability of functional equations with respect to bounded distributions (J.-U. Chung) -- 6. Stability of multi-Jensen mappings in non-Archimedean normed spaces (K. Cieplinski) -- 7. On stability of the equation of homogeneous functions on topological spaces (S. Czerwik) -- 8. Hyers-Ulam stability of the quadratic functional equation (E. Elhoucien, M. Youssef, T. M. Rassias) -- 9. Intuitionistic fuzzy approximately additive mappings (M. Eshaghi-Gordji, H. Khodaei, H. Baghani, M. Ramezani) -- 10. Stability of the pexiderized Cauchy functional equation in non-Archimedean spaces (G. Z. Eskandani, P. Gavruta) -- 11. Generalized Hyers-Ulam stability for general quadratic functional equation in quasi-Banach spaces (J. Gao) -- 12. Ulam stability problem for frames (L. Gavruta, P. Gavruta) -- 13. Generalized Hyers-Ulam stability of a quadratic functional equation (K.-W. Jun, H-M. Kim, J. Son) -- 14. On the Hyers-Ulam-Rassias stability of the bi-Pexider functional equation (K.-W. Jun, Y.-H. Lee) -- 15. Approximately midconvex functions (K. Misztal, J. Tabor, J. Tabor) -- 16. The Hyers-Ulam and Ger type stabilities of the first order linear differential equations (T. Miura, G. Hirasawa) -- 17. On the Butler-Rassias functional equation and its generalized Hyers-Ulam stability (T. Miura, G. Hirasawa, T. Hayata) -- 18. A note on the stability of an integral equation (T. Miura, G. Hirasawa, S.-E. Takahasi, T. Hayata) -- 19. On the stability of polynomial equations (A. Najati, T. M. Rassias) -- 20. Isomorphisms and derivations in proper JCQ*-triples (C. Park, M. Eshaghi-Gordji) -- 21. Fuzzy stability of an additive-quartic functional equation: a fixed point approach (C. Park, T.M. Rassias) -- 22. Selections of set-valued maps satisfying functional inclusions on square-symmetric grupoids (D. Popa) -- 23. On stability of isometries in Banach spaces (V.Y. Protasov) -- 24. Ulam stability of the operatorial equations (I.A. Rus) -- 25. Stability of the quadratic-cubic functional equation in quasi-Banach spaces (Z. Wang, W. Zhang) -- 26. u-trigonometric functional equations and Hyers-Ulam stability problem in hypergroups (D. Zeglami, S. Kabbaj, A. Charifi, A. Roukbi) -- 27. On multivariate Ostrowski type inequalities (Z Changjian, W.-S. Cheung) -- 28. Ternary semigroups and ternary algebras (A. Chronowski) -- 29. Popoviciu type functional equations on groups (M. Chudziak) -- 30. Norm and numerical radius inequalities for two linear operators in Hillbert spaces: a survey of recent results (S.S. Dragomir) -- 31. Cauchy’s functional equation and nowhere continuous/everywhere dense Costas bijections in Euclidean spaces (K. Drakakis) -- 32. On solutions of some generalizations of the Golab-Schinzel equation (E. Jablonska) -- 33. One-parameter groups of formal power series of one indeterminate (W. Jablonski) -- 34. On some problems concerning a sum type operator (H.H. Kairies) -- 35. Priors on the space of unimodal probability measures (G. Kouvaras, G. Kokolakis) -- 36. Generalized weighted arithmetic means (J. Matkowski) -- 37. On means which are quasi-arithmetic and of the Beckenbach-Gini type (J. Matkowski) -- 38. Scalar Riemann-Hillbert problem for multiply connected domains (V.V. Mityushev) -- 39. Hodge theory for Riemannian solenoids (V. Muñoz, R.P. Marco) -- 40. On solutions of a generalization of the Golab-Schinzel functional equation (A. Murenko) -- 41. On functional equation containing an indexed family of unknown mappings (P. Nath, D.K. Singh) -- 42. Two-step iterative method for nonconvex bifunction variational inequalities (M.A. Noor, K.I. Noor, E. Al-Said) -- 43. On a Sincov type functional equation (P. K. Sahoo) -- 44. Invariance in some families of means (G. Toader, I. Costin, S. Toader) -- 45. On a Hillbert-type integral inequality (B. Yang) -- 46. An extension of Hardy-Hillbert’s inequality (B. Yang) -- 47. A relation to Hillbert’s integral inequality and a basic Hillbert-type inequality (B. Yang, T.M. Rassias) En línea: http://dx.doi.org/10.1007/978-1-4614-0055-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32732 Ejemplares
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Título : Functional Analysis : Fundamentals and Applications Tipo de documento: documento electrónico Autores: Willem, Michel ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Birkhäuser Colección: Cornerstones, ISSN 2197-182X Número de páginas: XIII, 213 p. 18 illus Il.: online resource ISBN/ISSN/DL: 978-1-4614-7004-5 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Partial differential equations Differential Equations Mathematics, general Clasificación: 51 Matemáticas Resumen: The goal of this work is to present the principles of functional analysis in a clear and concise way. The first three chapters of Functional Analysis: Fundamentals and Applications describe the general notions of distance, integral and norm, as well as their relations. The three chapters that follow deal with fundamental examples: Lebesgue spaces, dual spaces and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the Pólya-Szego and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional analysis, in relation with integration and differentiation. Starting from elementary analysis and introducing relevant recent research, this work is an excellent resource for students in mathematics and applied mathematics Nota de contenido: Preface -- The Integral -- Norm -- Lebesgue Spaces -- Duality -- Sobolev Spaces -- Capacity -- Elliptic Problems -- Appendix -- Epilogue -- References -- Index of Notations -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-7004-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32333 Functional Analysis : Fundamentals and Applications [documento electrónico] / Willem, Michel ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Birkhäuser, 2013 . - XIII, 213 p. 18 illus : online resource. - (Cornerstones, ISSN 2197-182X) .
ISBN : 978-1-4614-7004-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Partial differential equations Differential Equations Mathematics, general Clasificación: 51 Matemáticas Resumen: The goal of this work is to present the principles of functional analysis in a clear and concise way. The first three chapters of Functional Analysis: Fundamentals and Applications describe the general notions of distance, integral and norm, as well as their relations. The three chapters that follow deal with fundamental examples: Lebesgue spaces, dual spaces and Sobolev spaces. Two subsequent chapters develop applications to capacity theory and elliptic problems. In particular, the isoperimetric inequality and the Pólya-Szego and Faber-Krahn inequalities are proved by purely functional methods. The epilogue contains a sketch of the history of functional analysis, in relation with integration and differentiation. Starting from elementary analysis and introducing relevant recent research, this work is an excellent resource for students in mathematics and applied mathematics Nota de contenido: Preface -- The Integral -- Norm -- Lebesgue Spaces -- Duality -- Sobolev Spaces -- Capacity -- Elliptic Problems -- Appendix -- Epilogue -- References -- Index of Notations -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-7004-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32333 Ejemplares
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Título : Functional Analysis in Asymmetric Normed Spaces Tipo de documento: documento electrónico Autores: Cobzas, Stefan ; SpringerLink (Online service) Editorial: Basel : Springer Basel Fecha de publicación: 2013 Otro editor: Imprint: Birkhäuser Colección: Frontiers in Mathematics, ISSN 1660-8046 Número de páginas: X, 219 p. 1 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-0348-0478-3 Idioma : Inglés (eng) Palabras clave: Mathematics Approximation theory Functional analysis Operator Topology Analysis Approximations and Expansions Theory Clasificación: 51 Matemáticas Resumen: An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, is merely a convex cone in the vector space of all linear functionals on X. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplay between the asymmetric norm p and its conjugate. Among the positive results one can mention: Hahn–Banach type theorems and separation results for convex sets, Krein–Milman type theorems, analogs of the fundamental principles – open mapping, closed graph and uniform boundedness theorems – an analog of the Schauder’s theorem on the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, one considers normed lattices equipped with asymmetric norms and spaces of semi-Lipschitz functions on quasi-metric spaces. Since the basic topological tools come from quasi-metric spaces and quasi-uniform spaces, the first chapter of the book contains a detailed presentation of some basic results from the theory of these spaces. The focus is on results which are most used in functional analysis – completeness, compactness and Baire category – which drastically differ from those in metric or uniform spaces. The book is fairly self-contained, the prerequisites being the acquaintance with the basic results in topology and functional analysis, so it may be used for an introduction to the subject. Since new results, in the focus of current research, are also included, researchers in the area can use it as a reference text Nota de contenido: Introduction.- 1. Quasi-metric and Quasi-uniform Spaces. 1.1. Topological properties of quasi-metric and quasi-uniform spaces -- 1.2. Completeness and compactness in quasi-metric and quasi-uniform spaces.- 2. Asymmetric Functional Analysis -- 2.1. Continuous linear operators between asymmetric normed spaces -- 2.2. Hahn-Banach type theorems and the separation of convex sets -- 2.3. The fundamental principles -- 2.4. Weak topologies -- 2.5. Applications to best approximation -- 2.6. Spaces of semi-Lipschitz functions -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0478-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32419 Functional Analysis in Asymmetric Normed Spaces [documento electrónico] / Cobzas, Stefan ; SpringerLink (Online service) . - Basel : Springer Basel : Imprint: Birkhäuser, 2013 . - X, 219 p. 1 illus. in color : online resource. - (Frontiers in Mathematics, ISSN 1660-8046) .
ISBN : 978-3-0348-0478-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Approximation theory Functional analysis Operator Topology Analysis Approximations and Expansions Theory Clasificación: 51 Matemáticas Resumen: An asymmetric norm is a positive definite sublinear functional p on a real vector space X. The topology generated by the asymmetric norm p is translation invariant so that the addition is continuous, but the asymmetry of the norm implies that the multiplication by scalars is continuous only when restricted to non-negative entries in the first argument. The asymmetric dual of X, meaning the set of all real-valued upper semi-continuous linear functionals on X, is merely a convex cone in the vector space of all linear functionals on X. In spite of these differences, many results from classical functional analysis have their counterparts in the asymmetric case, by taking care of the interplay between the asymmetric norm p and its conjugate. Among the positive results one can mention: Hahn–Banach type theorems and separation results for convex sets, Krein–Milman type theorems, analogs of the fundamental principles – open mapping, closed graph and uniform boundedness theorems – an analog of the Schauder’s theorem on the compactness of the conjugate mapping. Applications are given to best approximation problems and, as relevant examples, one considers normed lattices equipped with asymmetric norms and spaces of semi-Lipschitz functions on quasi-metric spaces. Since the basic topological tools come from quasi-metric spaces and quasi-uniform spaces, the first chapter of the book contains a detailed presentation of some basic results from the theory of these spaces. The focus is on results which are most used in functional analysis – completeness, compactness and Baire category – which drastically differ from those in metric or uniform spaces. The book is fairly self-contained, the prerequisites being the acquaintance with the basic results in topology and functional analysis, so it may be used for an introduction to the subject. Since new results, in the focus of current research, are also included, researchers in the area can use it as a reference text Nota de contenido: Introduction.- 1. Quasi-metric and Quasi-uniform Spaces. 1.1. Topological properties of quasi-metric and quasi-uniform spaces -- 1.2. Completeness and compactness in quasi-metric and quasi-uniform spaces.- 2. Asymmetric Functional Analysis -- 2.1. Continuous linear operators between asymmetric normed spaces -- 2.2. Hahn-Banach type theorems and the separation of convex sets -- 2.3. The fundamental principles -- 2.4. Weak topologies -- 2.5. Applications to best approximation -- 2.6. Spaces of semi-Lipschitz functions -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-3-0348-0478-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32419 Ejemplares
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