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Título : Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces Tipo de documento: documento electrónico Autores: Diagana, Toka ; SpringerLink (Online service) Editorial: Cham : Springer International Publishing Fecha de publicación: 2013 Otro editor: Imprint: Springer Número de páginas: XIV, 303 p Il.: online resource ISBN/ISSN/DL: 978-3-319-00849-3 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Operator theory Differential equations Partial differential Ordinary Equations Theory Abstract Analysis Clasificación: 51 Matemáticas Resumen: This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standard references that currently exist on those new classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basic introductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers in mathematics as well as in engineering, in physics, and related areas. Further, some parts of the book may be used for various graduate and undergraduate courses Nota de contenido: 1. Metric, Banach, and Hilbert Spaces -- 2. Linear Operators on Banach Spaces -- 3. Almost Periodic Functions -- 4. Almost Automorphic Functions -- 5. Pseudo-Almost Periodic Functions -- 6. Pseudo-Almost Automorphic Functions -- 7. Existence Results for Some Second-Order Differential Equations -- 8. Existence Results to Some Integrodifferential Equations -- 9. Existence of C(m)-Pseudo-Almost Automorphic Solutions -- 10. Pseudo-Almost Periodic Solutions to Some Third-Order Differential Equations -- 11. Pseudo-Almost Automorphic Solutions to Some Sobolev-Type Equations -- 12. Stability Results for Some Higher-Order Difference Equations -- 13. Appendix A -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-319-00849-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32467 Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces [documento electrónico] / Diagana, Toka ; SpringerLink (Online service) . - Cham : Springer International Publishing : Imprint: Springer, 2013 . - XIV, 303 p : online resource.
ISBN : 978-3-319-00849-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Operator theory Differential equations Partial differential Ordinary Equations Theory Abstract Analysis Clasificación: 51 Matemáticas Resumen: This book presents a comprehensive introduction to the concepts of almost periodicity, asymptotic almost periodicity, almost automorphy, asymptotic almost automorphy, pseudo-almost periodicity, and pseudo-almost automorphy as well as their recent generalizations. Some of the results presented are either new or else cannot be easily found in the mathematical literature. Despite the noticeable and rapid progress made on these important topics, the only standard references that currently exist on those new classes of functions and their applications are still scattered research articles. One of the main objectives of this book is to close that gap. The prerequisites for the book is the basic introductory course in real analysis. Depending on the background of the student, the book may be suitable for a beginning graduate and/or advanced undergraduate student. Moreover, it will be of a great interest to researchers in mathematics as well as in engineering, in physics, and related areas. Further, some parts of the book may be used for various graduate and undergraduate courses Nota de contenido: 1. Metric, Banach, and Hilbert Spaces -- 2. Linear Operators on Banach Spaces -- 3. Almost Periodic Functions -- 4. Almost Automorphic Functions -- 5. Pseudo-Almost Periodic Functions -- 6. Pseudo-Almost Automorphic Functions -- 7. Existence Results for Some Second-Order Differential Equations -- 8. Existence Results to Some Integrodifferential Equations -- 9. Existence of C(m)-Pseudo-Almost Automorphic Solutions -- 10. Pseudo-Almost Periodic Solutions to Some Third-Order Differential Equations -- 11. Pseudo-Almost Automorphic Solutions to Some Sobolev-Type Equations -- 12. Stability Results for Some Higher-Order Difference Equations -- 13. Appendix A -- References -- Index En línea: http://dx.doi.org/10.1007/978-3-319-00849-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32467 Ejemplares
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Título : Representations, Wavelets, and Frames : A Celebration of the Mathematical Work of Lawrence W. Baggett Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Jorgensen, Palle E. T ; Merrill, Kathy D ; Packer, Judith A Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2008 Colección: Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Número de páginas: XL, 324 p. 22 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4683-7 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Fourier Functional Applied mathematics Engineering Mathematical models Modeling and Industrial Analysis Signal, Image Speech Processing Abstract Applications of Clasificación: 51 Matemáticas Resumen: Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be orthogonal or have redundancies (e.g., frames from signal analysis). Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers. The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, and concludes with analyses of computational schemes used in communications engineering. Within each section, individual chapters present new research, provide relevant background material, and point to new trends and open questions. Contributors: C. Benson, M. Bownik, V. Furst, V.W. Guillemin, B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornelson, J.D. Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D.W. Stroock, K.F. Taylor, E. Weber, X. Zhang Nota de contenido: Classical and Abstract Harmonic Analysis -- Some Riemann Sums Are Better Than Others -- Gelfand Pairs Associated with Finite Heisenberg Groups -- Groups with Atomic Regular Representation -- Wavelet Transforms and Admissible Group Representations -- Frames and Multiresolution Structures -- The Density Theorem and the Homogeneous Approximation Property for Gabor Frames -- Recent Developments on Dual Wavelet Frames -- Characteristic Wavelet Equations and Generalizations of the Spectral Function -- Baggett’s Problem for Frame Wavelets -- Wavelet Sets -- Simple Wavelet Sets for Scalar Dilations in ?2 -- Interpolation Maps and Congruence Domains for Wavelet Sets -- Applications to Dynamical Systems and C*-Algebras -- Orthogonal Exponentials for Bernoulli Iterated Function Systems -- A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice -- Signal and Image Processing -- Sampling and Time-Frequency Localization of Band-Limited and Multiband Signals -- Entropy Encoding in Wavelet Image Compression En línea: http://dx.doi.org/10.1007/978-0-8176-4683-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34277 Representations, Wavelets, and Frames : A Celebration of the Mathematical Work of Lawrence W. Baggett [documento electrónico] / SpringerLink (Online service) ; Jorgensen, Palle E. T ; Merrill, Kathy D ; Packer, Judith A . - Boston, MA : Birkhäuser Boston, 2008 . - XL, 324 p. 22 illus : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) .
ISBN : 978-0-8176-4683-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Fourier Functional Applied mathematics Engineering Mathematical models Modeling and Industrial Analysis Signal, Image Speech Processing Abstract Applications of Clasificación: 51 Matemáticas Resumen: Motivated by applications, an underlying theme in analysis is that of finding bases and understanding the transforms that implement them. These may be based on Fourier techniques or involve wavelet tools; they may be orthogonal or have redundancies (e.g., frames from signal analysis). Representations, Wavelets, and Frames contains chapters pertaining to this theme from experts and expositors of renown in mathematical analysis and representation theory. Topics are selected with an emphasis on fundamental and timeless techniques with a geometric and spectral-theoretic flavor. The material is self-contained and presented in a pedagogical style that is accessible to students from both pure and applied mathematics while also of interest to engineers. The book is organized into five sections that move from the theoretical underpinnings of the subject, through geometric connections to tilings, lattices and fractals, and concludes with analyses of computational schemes used in communications engineering. Within each section, individual chapters present new research, provide relevant background material, and point to new trends and open questions. Contributors: C. Benson, M. Bownik, V. Furst, V.W. Guillemin, B. Han, C. Heil, J.A. Hogan, P.E.T. Jorgensen, K. Kornelson, J.D. Lakey, D.R. Larson, K.D. Merrill, J.A. Packer, G. Ratcliff, K. Shuman, M.-S. Song, D.W. Stroock, K.F. Taylor, E. Weber, X. Zhang Nota de contenido: Classical and Abstract Harmonic Analysis -- Some Riemann Sums Are Better Than Others -- Gelfand Pairs Associated with Finite Heisenberg Groups -- Groups with Atomic Regular Representation -- Wavelet Transforms and Admissible Group Representations -- Frames and Multiresolution Structures -- The Density Theorem and the Homogeneous Approximation Property for Gabor Frames -- Recent Developments on Dual Wavelet Frames -- Characteristic Wavelet Equations and Generalizations of the Spectral Function -- Baggett’s Problem for Frame Wavelets -- Wavelet Sets -- Simple Wavelet Sets for Scalar Dilations in ?2 -- Interpolation Maps and Congruence Domains for Wavelet Sets -- Applications to Dynamical Systems and C*-Algebras -- Orthogonal Exponentials for Bernoulli Iterated Function Systems -- A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice -- Signal and Image Processing -- Sampling and Time-Frequency Localization of Band-Limited and Multiband Signals -- Entropy Encoding in Wavelet Image Compression En línea: http://dx.doi.org/10.1007/978-0-8176-4683-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34277 Ejemplares
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Título : A Basis Theory Primer : Expanded Edition Tipo de documento: documento electrónico Autores: Heil, Christopher ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2011 Colección: Applied and Numerical Harmonic Analysis Número de páginas: XXV, 537 p. 42 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4687-5 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Fourier Functional Applied mathematics Engineering Abstract Analysis Appl.Mathematics/Computational Methods of Applications Signal, Image and Speech Processing Clasificación: 51 Matemáticas Resumen: The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and its use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. * Part I develops the functional analysis that underlies most of the concepts presented in the later parts of the text. * Part II presents the abstract theory of bases and frames in Banach and Hilbert spaces, including the classical topics of convergence, Schauder bases, biorthogonal systems, and unconditional bases, followed by the more recent topics of Riesz bases and frames in Hilbert spaces. * Part III relates bases and frames to applied harmonic analysis, including sampling theory, Gabor analysis, and wavelet theory. * Part IV deals with classical harmonic analysis and Fourier series, emphasizing the role played by bases, which is a different viewpoint from that taken in most discussions of Fourier series. Key features: * Self-contained presentation with clear proofs accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications. * Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses; hints for selected exercises are included at the end of the book. * A separate solutions manual is available for instructors upon request at: www.birkhauser-science.com/978-0-8176-4686-8/. * No other text develops the ties between classical basis theory and its modern uses in applied harmonic analysis. A Basis Theory Primer is suitable for independent study or as the basis for a graduate-level course. Instructors have several options for building a course around the text depending on the level and background of their students Nota de contenido: ANHA Series Preface -- Preface -- General Notation -- Part I. A Primer on Functional Analysis -- Banach Spaces and Operator Theory -- Functional Analysis -- Part II. Bases and Frames -- Unconditional Convergence of Series in Banach and Hilbert Spaces -- Bases in Banach Spaces -- Biorthogonality, Minimality, and More About Bases -- Unconditional Bases in Banach Spaces -- Bessel Sequences and Bases in Hilbert Spaces -- Frames in Hilbert Spaces -- Part III. Bases and Frames in Applied Harmonic Analysis -- The Fourier Transform on the Real Line -- Sampling, Weighted Exponentials, and Translations -- Gabor Bases and Frames -- Wavelet Bases and Frames -- Part IV. Fourier Series -- Fourier Series -- Basic Properties of Fourier Series -- Part V. Appendices -- Lebesgue Measure and Integration -- Compact and Hilbert–Schmidt Operators -- Hints for Exercises -- Index of Symbols -- References -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-4687-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33088 A Basis Theory Primer : Expanded Edition [documento electrónico] / Heil, Christopher ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2011 . - XXV, 537 p. 42 illus : online resource. - (Applied and Numerical Harmonic Analysis) .
ISBN : 978-0-8176-4687-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Fourier Functional Applied mathematics Engineering Abstract Analysis Appl.Mathematics/Computational Methods of Applications Signal, Image and Speech Processing Clasificación: 51 Matemáticas Resumen: The classical subject of bases in Banach spaces has taken on a new life in the modern development of applied harmonic analysis. This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and its use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. * Part I develops the functional analysis that underlies most of the concepts presented in the later parts of the text. * Part II presents the abstract theory of bases and frames in Banach and Hilbert spaces, including the classical topics of convergence, Schauder bases, biorthogonal systems, and unconditional bases, followed by the more recent topics of Riesz bases and frames in Hilbert spaces. * Part III relates bases and frames to applied harmonic analysis, including sampling theory, Gabor analysis, and wavelet theory. * Part IV deals with classical harmonic analysis and Fourier series, emphasizing the role played by bases, which is a different viewpoint from that taken in most discussions of Fourier series. Key features: * Self-contained presentation with clear proofs accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications. * Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses; hints for selected exercises are included at the end of the book. * A separate solutions manual is available for instructors upon request at: www.birkhauser-science.com/978-0-8176-4686-8/. * No other text develops the ties between classical basis theory and its modern uses in applied harmonic analysis. A Basis Theory Primer is suitable for independent study or as the basis for a graduate-level course. Instructors have several options for building a course around the text depending on the level and background of their students Nota de contenido: ANHA Series Preface -- Preface -- General Notation -- Part I. A Primer on Functional Analysis -- Banach Spaces and Operator Theory -- Functional Analysis -- Part II. Bases and Frames -- Unconditional Convergence of Series in Banach and Hilbert Spaces -- Bases in Banach Spaces -- Biorthogonality, Minimality, and More About Bases -- Unconditional Bases in Banach Spaces -- Bessel Sequences and Bases in Hilbert Spaces -- Frames in Hilbert Spaces -- Part III. Bases and Frames in Applied Harmonic Analysis -- The Fourier Transform on the Real Line -- Sampling, Weighted Exponentials, and Translations -- Gabor Bases and Frames -- Wavelet Bases and Frames -- Part IV. Fourier Series -- Fourier Series -- Basic Properties of Fourier Series -- Part V. Appendices -- Lebesgue Measure and Integration -- Compact and Hilbert–Schmidt Operators -- Hints for Exercises -- Index of Symbols -- References -- Index En línea: http://dx.doi.org/10.1007/978-0-8176-4687-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33088 Ejemplares
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Título : Frames and Bases : An Introductory Course Tipo de documento: documento electrónico Autores: Christensen, Ole ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2008 Colección: Applied and Numerical Harmonic Analysis Número de páginas: XVIII, 313 p. 14 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4678-3 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Fourier Functional Operator theory Mathematical models Analysis Modeling and Industrial Signal, Image Speech Processing Abstract Theory Clasificación: 51 Matemáticas Resumen: During the last several years, frames have become increasingly popular; they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of these constructions were based on quite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to a more constructive one. Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. Key features and topics: * Results presented in an accessible way for graduate students, pure and applied mathematicians as well as engineers. * An introductory chapter provides basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces. * Extensive exercises for use in theoretical graduate courses on bases and frames, or applications-oriented courses focusing on either Gabor analysis or wavelets. * Detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames. * Content split naturally into two parts: The first part describes the theory on an abstract level, whereas the second part deals with explicit constructions of frames with applications and connections to time-frequency analysis, Gabor analysis, and wavelets. Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource Nota de contenido: Frames in Finite-dimensional Inner Product Spaces -- Infinite-dimensional Vector Spaces and Sequences -- Bases -- Bases and their Limitations -- Frames in Hilbert Spaces -- B-splines -- Frames of Translates -- Shift-Invariant Systems -- Gabor Frames in L(R) -- Gabor Frames in l(Z) -- Wavelet Frames in L(R) En línea: http://dx.doi.org/10.1007/978-0-8176-4678-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34275 Frames and Bases : An Introductory Course [documento electrónico] / Christensen, Ole ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2008 . - XVIII, 313 p. 14 illus : online resource. - (Applied and Numerical Harmonic Analysis) .
ISBN : 978-0-8176-4678-3
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Fourier Functional Operator theory Mathematical models Analysis Modeling and Industrial Signal, Image Speech Processing Abstract Theory Clasificación: 51 Matemáticas Resumen: During the last several years, frames have become increasingly popular; they have appeared in a large number of applications, and several concrete constructions of frames of various types have been presented. Most of these constructions were based on quite direct methods rather than the classical sufficient conditions for obtaining a frame. Consequently, there is a need for an updated book on frames, which moves the focus from the classical approach to a more constructive one. Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. Key features and topics: * Results presented in an accessible way for graduate students, pure and applied mathematicians as well as engineers. * An introductory chapter provides basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces. * Extensive exercises for use in theoretical graduate courses on bases and frames, or applications-oriented courses focusing on either Gabor analysis or wavelets. * Detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames. * Content split naturally into two parts: The first part describes the theory on an abstract level, whereas the second part deals with explicit constructions of frames with applications and connections to time-frequency analysis, Gabor analysis, and wavelets. Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource Nota de contenido: Frames in Finite-dimensional Inner Product Spaces -- Infinite-dimensional Vector Spaces and Sequences -- Bases -- Bases and their Limitations -- Frames in Hilbert Spaces -- B-splines -- Frames of Translates -- Shift-Invariant Systems -- Gabor Frames in L(R) -- Gabor Frames in l(Z) -- Wavelet Frames in L(R) En línea: http://dx.doi.org/10.1007/978-0-8176-4678-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34275 Ejemplares
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Título : Geometric Function Theory : Explorations in Complex Analysis Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Krantz, Steven G 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) ; Krantz, Steven G . - 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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