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Autor Steven G. Krantz |
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Título : Explorations in Harmonic Analysis : with Applications to Complex Function Theory and the Heisenberg Group Tipo de documento: documento electrónico Autores: Steven G. Krantz ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2009 Colección: Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Número de páginas: XIV, 362 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4669-1 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Harmonic analysis Approximation Fourier Functions of complex variables Mathematical models Abstract Analysis Modeling and Industrial Approximations Expansions Several Complex Variables Analytic Spaces Theory Generalizations Clasificación: 51 Matemáticas Resumen: This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis. Within the textbook, the new ideas on the Heisenberg group are applied to the study of estimates for both the Szegö and Poisson–Szegö integrals on the unit ball in complex space. Thus the main theme of the book is also tied into complex analysis of several variables. With a rigorous but well-paced exposition, this text provides all the necessary background in singular and fractional integrals, as well as Hardy spaces and the function theory of several complex variables, needed to understand Heisenberg analysis. Explorations in Harmonic Analysis is ideal for graduate students in mathematics, physics, and engineering. Prerequisites include a fundamental background in real and complex analysis and some exposure to functional analysis Nota de contenido: Ontology and History of Real Analysis -- The Central Idea: The Hilbert Transform -- Essentials of the Fourier Transform -- Fractional and Singular Integrals -- A Crash Course in Several Complex Variables -- Pseudoconvexity and Domains of Holomorphy -- Canonical Complex Integral Operators -- Hardy Spaces Old and New -- to the Heisenberg Group -- Analysis on the Heisenberg Group -- A Coda on Domains of Finite Type En línea: http://dx.doi.org/10.1007/978-0-8176-4669-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33939 Explorations in Harmonic Analysis : with Applications to Complex Function Theory and the Heisenberg Group [documento electrónico] / Steven G. Krantz ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston, 2009 . - XIV, 362 p : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) .
ISBN : 978-0-8176-4669-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Harmonic analysis Approximation Fourier Functions of complex variables Mathematical models Abstract Analysis Modeling and Industrial Approximations Expansions Several Complex Variables Analytic Spaces Theory Generalizations Clasificación: 51 Matemáticas Resumen: This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis. Within the textbook, the new ideas on the Heisenberg group are applied to the study of estimates for both the Szegö and Poisson–Szegö integrals on the unit ball in complex space. Thus the main theme of the book is also tied into complex analysis of several variables. With a rigorous but well-paced exposition, this text provides all the necessary background in singular and fractional integrals, as well as Hardy spaces and the function theory of several complex variables, needed to understand Heisenberg analysis. Explorations in Harmonic Analysis is ideal for graduate students in mathematics, physics, and engineering. Prerequisites include a fundamental background in real and complex analysis and some exposure to functional analysis Nota de contenido: Ontology and History of Real Analysis -- The Central Idea: The Hilbert Transform -- Essentials of the Fourier Transform -- Fractional and Singular Integrals -- A Crash Course in Several Complex Variables -- Pseudoconvexity and Domains of Holomorphy -- Canonical Complex Integral Operators -- Hardy Spaces Old and New -- to the Heisenberg Group -- Analysis on the Heisenberg Group -- A Coda on Domains of Finite Type En línea: http://dx.doi.org/10.1007/978-0-8176-4669-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33939 Ejemplares
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Título : Geometric Analysis of the Bergman Kernel and Metric Tipo de documento: documento electrónico Autores: Steven G. Krantz ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 268 Número de páginas: XIII, 292 p. 7 illus Il.: online resource ISBN/ISSN/DL: 978-1-4614-7924-6 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Partial differential equations Differential geometry Equations Geometry Clasificación: 51 Matemáticas Resumen: This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory Nota de contenido: Preface -- 1. Introductory Ideas -- 2. The Bergman Metric -- 3. Geometric and Analytic Ideas -- 4. Partial Differential Equations -- 5. Further Geometric Explorations -- 6. Additional Analytic Topics -- 7. Curvature of the Bergman Metric -- 8. Concluding Remarks -- Table of Notation -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-7924-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32372 Geometric Analysis of the Bergman Kernel and Metric [documento electrónico] / Steven G. Krantz ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XIII, 292 p. 7 illus : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 268) .
ISBN : 978-1-4614-7924-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functional Partial differential equations Differential geometry Equations Geometry Clasificación: 51 Matemáticas Resumen: This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory Nota de contenido: Preface -- 1. Introductory Ideas -- 2. The Bergman Metric -- 3. Geometric and Analytic Ideas -- 4. Partial Differential Equations -- 5. Further Geometric Explorations -- 6. Additional Analytic Topics -- 7. Curvature of the Bergman Metric -- 8. Concluding Remarks -- Table of Notation -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-7924-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32372 Ejemplares
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Título : Geometric Function Theory : Explorations in Complex Analysis Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Steven G. Krantz Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2006 Colección: Cornerstones Número de páginas: XIII, 314 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4440-6 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Harmonic Functions of complex variables Partial differential equations Potential theory Differential geometry a Complex Variable Abstract Geometry Equations Theory Clasificación: 51 Matemáticas Resumen: Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous Cauchy–Riemann equations, and the corona problem. The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme. This methodically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysis—and also to spark the interest of seasoned workers in the field—the book imparts a solid education both in complex analysis and in how modern mathematics works Nota de contenido: Classical Function Theory -- Invariant Geometry -- Variations on the Theme of the Schwarz Lemma -- Normal Families -- The Riemann Mapping Theorem and Its Generalizations -- Boundary Regularity of Conformal Maps -- The Boundary Behavior of Holomorphic Functions -- Real and Harmonic Analysis -- The Cauchy-Riemann Equations -- The Green’s Function and the Poisson Kernel -- Harmonic Measure -- Conjugate Functions and the Hilbert Transform -- Wolff’s Proof of the Corona Theorem -- Algebraic Topics -- Automorphism Groups of Domains in the Plane -- Cousin Problems, Cohomology, and Sheaves En línea: http://dx.doi.org/10.1007/0-8176-4440-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34852 Geometric Function Theory : Explorations in Complex Analysis [documento electrónico] / SpringerLink (Online service) ; Steven G. Krantz . - Boston, MA : Birkhäuser Boston, 2006 . - XIII, 314 p : online resource. - (Cornerstones) .
ISBN : 978-0-8176-4440-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Harmonic Functions of complex variables Partial differential equations Potential theory Differential geometry a Complex Variable Abstract Geometry Equations Theory Clasificación: 51 Matemáticas Resumen: Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous Cauchy–Riemann equations, and the corona problem. The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme. This methodically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysis—and also to spark the interest of seasoned workers in the field—the book imparts a solid education both in complex analysis and in how modern mathematics works Nota de contenido: Classical Function Theory -- Invariant Geometry -- Variations on the Theme of the Schwarz Lemma -- Normal Families -- The Riemann Mapping Theorem and Its Generalizations -- Boundary Regularity of Conformal Maps -- The Boundary Behavior of Holomorphic Functions -- Real and Harmonic Analysis -- The Cauchy-Riemann Equations -- The Green’s Function and the Poisson Kernel -- Harmonic Measure -- Conjugate Functions and the Hilbert Transform -- Wolff’s Proof of the Corona Theorem -- Algebraic Topics -- Automorphism Groups of Domains in the Plane -- Cousin Problems, Cohomology, and Sheaves En línea: http://dx.doi.org/10.1007/0-8176-4440-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34852 Ejemplares
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Título : Geometric Integration Theory Tipo de documento: documento electrónico Autores: Steven G. Krantz ; SpringerLink (Online service) ; Harold R. Parks Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2008 Colección: Cornerstones Número de páginas: XVI, 340 p. 33 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4679-0 Idioma : Inglés (eng) Palabras clave: Mathematics Integral equations transforms Operational calculus Measure theory Geometry Convex geometry Discrete Differential and Integration Equations Transforms, Calculus Clasificación: 51 Matemáticas Resumen: This textbook introduces geometric measure theory through the notion of currents. Currents—continuous linear functionals on spaces of differential forms—are a natural language in which to formulate various types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Key features of Geometric Integration Theory: * Includes topics on the deformation theorem, the area and coarea formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces * Applies techniques to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics * Provides considerable background material for the student Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for use in the classroom and for self-study. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for graduate students and researchers Nota de contenido: Basics -- Carathéodory’s Construction and Lower-Dimensional Measures -- Invariant Measures and the Construction of Haar Measure. -- Covering Theorems and the Differentiation of Integrals -- Analytical Tools: The Area Formula, the Coarea Formula, and Poincaré Inequalities. -- The Calculus of Differential Forms and Stokes’s Theorem -- to Currents -- Currents and the Calculus of Variations -- Regularity of Mass-Minimizing Currents En línea: http://dx.doi.org/10.1007/978-0-8176-4679-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34276 Geometric Integration Theory [documento electrónico] / Steven G. Krantz ; SpringerLink (Online service) ; Harold R. Parks . - Boston : Birkhäuser Boston, 2008 . - XVI, 340 p. 33 illus : online resource. - (Cornerstones) .
ISBN : 978-0-8176-4679-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Integral equations transforms Operational calculus Measure theory Geometry Convex geometry Discrete Differential and Integration Equations Transforms, Calculus Clasificación: 51 Matemáticas Resumen: This textbook introduces geometric measure theory through the notion of currents. Currents—continuous linear functionals on spaces of differential forms—are a natural language in which to formulate various types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Key features of Geometric Integration Theory: * Includes topics on the deformation theorem, the area and coarea formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces * Applies techniques to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics * Provides considerable background material for the student Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for use in the classroom and for self-study. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for graduate students and researchers Nota de contenido: Basics -- Carathéodory’s Construction and Lower-Dimensional Measures -- Invariant Measures and the Construction of Haar Measure. -- Covering Theorems and the Differentiation of Integrals -- Analytical Tools: The Area Formula, the Coarea Formula, and Poincaré Inequalities. -- The Calculus of Differential Forms and Stokes’s Theorem -- to Currents -- Currents and the Calculus of Variations -- Regularity of Mass-Minimizing Currents En línea: http://dx.doi.org/10.1007/978-0-8176-4679-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34276 Ejemplares
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Título : The Geometry of Complex Domains Tipo de documento: documento electrónico Autores: Robert E. Greene ; SpringerLink (Online service) ; Kang-Tae Kim ; Steven G. Krantz Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2011 Colección: Progress in Mathematics num. 291 Número de páginas: XIV, 303 p. 14 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4622-6 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Dynamics Ergodic theory Functions of complex variables Geometry Several Complex Variables and Analytic Spaces Dynamical Systems Theory Clasificación: 51 Matemáticas Resumen: The geometry of complex domains is a subject with roots extending back more than a century, to the uniformization theorem of Poincaré and Koebe and the resulting proof of existence of canonical metrics for hyperbolic Riemann surfaces. In modern times, developments in several complex variables by Bergman, Hörmander, Andreotti-Vesentini, Kohn, Fefferman, and others have opened up new possibilities for the unification of complex function theory and complex geometry. In particular, geometry can be used to study biholomorphic mappings in remarkable ways. This book presents a complete picture of these developments. Beginning with the one-variable case—background information which cannot be found elsewhere in one place—the book presents a complete picture of the symmetries of domains from the point of view of holomorphic mappings. It describes all the relevant techniques, from differential geometry to Lie groups to partial differential equations to harmonic analysis. Specific concepts addressed include: covering spaces and uniformization; Bergman geometry; automorphism groups; invariant metrics; the scaling method. All modern results are accompanied by detailed proofs, and many illustrative examples and figures appear throughout. Written by three leading experts in the field, The Geometry of Complex Domains is the first book to provide systematic treatment of recent developments in the subject of the geometry of complex domains and automorphism groups of domains. A unique and definitive work in this subject area, it will be a valuable resource for graduate students and a useful reference for researchers in the field Nota de contenido: Preface -- 1 Preliminaries -- 2 Riemann Surfaces and Covering Spaces -- 3 The Bergman Kernel and Metric -- 4 Applications of Bergman Geometry -- 5 Lie Groups Realized as Automorphism Groups -- 6 The Significance of Large Isotropy Groups -- 7 Some Other Invariant Metrics -- 8 Automorphism Groups and Classification of Reinhardt Domains -- 9 The Scaling Method, I -- 10 The Scaling Method, II -- 11 Afterword -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-4622-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33086 The Geometry of Complex Domains [documento electrónico] / Robert E. Greene ; SpringerLink (Online service) ; Kang-Tae Kim ; Steven G. Krantz . - Boston : Birkhäuser Boston, 2011 . - XIV, 303 p. 14 illus : online resource. - (Progress in Mathematics; 291) .
ISBN : 978-0-8176-4622-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Dynamics Ergodic theory Functions of complex variables Geometry Several Complex Variables and Analytic Spaces Dynamical Systems Theory Clasificación: 51 Matemáticas Resumen: The geometry of complex domains is a subject with roots extending back more than a century, to the uniformization theorem of Poincaré and Koebe and the resulting proof of existence of canonical metrics for hyperbolic Riemann surfaces. In modern times, developments in several complex variables by Bergman, Hörmander, Andreotti-Vesentini, Kohn, Fefferman, and others have opened up new possibilities for the unification of complex function theory and complex geometry. In particular, geometry can be used to study biholomorphic mappings in remarkable ways. This book presents a complete picture of these developments. Beginning with the one-variable case—background information which cannot be found elsewhere in one place—the book presents a complete picture of the symmetries of domains from the point of view of holomorphic mappings. It describes all the relevant techniques, from differential geometry to Lie groups to partial differential equations to harmonic analysis. Specific concepts addressed include: covering spaces and uniformization; Bergman geometry; automorphism groups; invariant metrics; the scaling method. All modern results are accompanied by detailed proofs, and many illustrative examples and figures appear throughout. Written by three leading experts in the field, The Geometry of Complex Domains is the first book to provide systematic treatment of recent developments in the subject of the geometry of complex domains and automorphism groups of domains. A unique and definitive work in this subject area, it will be a valuable resource for graduate students and a useful reference for researchers in the field Nota de contenido: Preface -- 1 Preliminaries -- 2 Riemann Surfaces and Covering Spaces -- 3 The Bergman Kernel and Metric -- 4 Applications of Bergman Geometry -- 5 Lie Groups Realized as Automorphism Groups -- 6 The Significance of Large Isotropy Groups -- 7 Some Other Invariant Metrics -- 8 Automorphism Groups and Classification of Reinhardt Domains -- 9 The Scaling Method, I -- 10 The Scaling Method, II -- 11 Afterword -- Bibliography -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-4622-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33086 Ejemplares
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