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Título : Spaces of Holomorphic Functions in the Unit Ball Tipo de documento: documento electrónico Autores: Kehe Zhu ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2005 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 226 Número de páginas: X, 274 p Il.: online resource ISBN/ISSN/DL: 978-0-387-27539-0 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functions of complex variables Several Complex Variables and Analytic Spaces Clasificación: 51 Matemáticas Resumen: There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. Spaces discussed include the Bergman spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov spaces, and the Lipschitz spaces. Most proofs in the book are new and simpler than the existing ones in the literature. The central idea in almost all these proofs is based on integral representations of holomorphic functions and elementary properties of the Bergman kernel, the Bergman metric, and the automorphism group. The unit ball was chosen as the setting since most results can be achieved there using straightforward formulas without much fuss. The book can be read comfortably by anyone familiar with single variable complex analysis; no prerequisite on several complex variables is required. The author has included exercises at the end of each chapter that vary greatly in the level of difficulty. Kehe Zhu is Professor of Mathematics at State University of New York at Albany. His previous books include Operator Theory in Function Spaces (Marcel Dekker 1990), Theory of Bergman Spaces, with H. Hedenmalm and B. Korenblum (Springer 2000), and An Introduction to Operator Algebras (CRC Press 1993) Nota de contenido: Preliminaries -- Bergman Spaces -- The Bloch Space -- Hardy Spaces -- Functions of Bounded Mean Oscillation -- Besov Spaces -- Lipschitz Spaces En línea: http://dx.doi.org/10.1007/0-387-27539-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35122 Spaces of Holomorphic Functions in the Unit Ball [documento electrónico] / Kehe Zhu ; SpringerLink (Online service) . - New York, NY : Springer New York, 2005 . - X, 274 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 226) .
ISBN : 978-0-387-27539-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Functions of complex variables Several Complex Variables and Analytic Spaces Clasificación: 51 Matemáticas Resumen: There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. Spaces discussed include the Bergman spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov spaces, and the Lipschitz spaces. Most proofs in the book are new and simpler than the existing ones in the literature. The central idea in almost all these proofs is based on integral representations of holomorphic functions and elementary properties of the Bergman kernel, the Bergman metric, and the automorphism group. The unit ball was chosen as the setting since most results can be achieved there using straightforward formulas without much fuss. The book can be read comfortably by anyone familiar with single variable complex analysis; no prerequisite on several complex variables is required. The author has included exercises at the end of each chapter that vary greatly in the level of difficulty. Kehe Zhu is Professor of Mathematics at State University of New York at Albany. His previous books include Operator Theory in Function Spaces (Marcel Dekker 1990), Theory of Bergman Spaces, with H. Hedenmalm and B. Korenblum (Springer 2000), and An Introduction to Operator Algebras (CRC Press 1993) Nota de contenido: Preliminaries -- Bergman Spaces -- The Bloch Space -- Hardy Spaces -- Functions of Bounded Mean Oscillation -- Besov Spaces -- Lipschitz Spaces En línea: http://dx.doi.org/10.1007/0-387-27539-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35122 Ejemplares
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Título : Analysis on Fock Spaces Tipo de documento: documento electrónico Autores: Kehe Zhu ; SpringerLink (Online service) Editorial: Boston, MA : Springer US Fecha de publicación: 2012 Otro editor: Imprint: Springer Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 263 Número de páginas: X, 346 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-8801-0 Idioma : Inglés (eng) Palabras clave: Mathematics Functional analysis Functions of complex variables Operator theory a Complex Variable Theory Several Variables and Analytic Spaces Analysis Clasificación: 51 Matemáticas Resumen: Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms “Hardy spaces” and “Bergman spaces” are by now standard and well established. But the term “Fock spaces” is a different story. Numerous excellent books now exist on the subject of Hardy spaces. Several books about Bergman spaces, including some of the author’s, have also appeared in the past few decades. But there has been no book on the market concerning the Fock spaces. The purpose of this book is to fill that void, especially when many results in the subject are complete by now. This book presents important results and techniques summarized in one place, so that newcomers, especially graduate students, have a convenient reference to the subject. This book contains proofs that are new and simpler than the existing ones in the literature. In particular, the book avoids the use of the Heisenberg group, the Fourier transform, and the heat equation. This helps to keep the prerequisites to a minimum. A standard graduate course in each of real analysis, complex analysis, and functional analysis should be sufficient preparation for the reader Nota de contenido: Preface -- Chapter 1. Preliminaries -- Chapter 2. Fock Spaces -- Chapter 3. The Berezin Transform and BMO -- Chapter 4. Interpolating and Sampling Sequences -- Chapter 5. Zero Sets for Fock Spaces -- Chapter 6. Toeplitz Operators -- Chapter 7. Small Hankel Operators -- Chapter 8. Hankel Operators -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-8801-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32711 Analysis on Fock Spaces [documento electrónico] / Kehe Zhu ; SpringerLink (Online service) . - Boston, MA : Springer US : Imprint: Springer, 2012 . - X, 346 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 263) .
ISBN : 978-1-4419-8801-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Functional analysis Functions of complex variables Operator theory a Complex Variable Theory Several Variables and Analytic Spaces Analysis Clasificación: 51 Matemáticas Resumen: Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms “Hardy spaces” and “Bergman spaces” are by now standard and well established. But the term “Fock spaces” is a different story. Numerous excellent books now exist on the subject of Hardy spaces. Several books about Bergman spaces, including some of the author’s, have also appeared in the past few decades. But there has been no book on the market concerning the Fock spaces. The purpose of this book is to fill that void, especially when many results in the subject are complete by now. This book presents important results and techniques summarized in one place, so that newcomers, especially graduate students, have a convenient reference to the subject. This book contains proofs that are new and simpler than the existing ones in the literature. In particular, the book avoids the use of the Heisenberg group, the Fourier transform, and the heat equation. This helps to keep the prerequisites to a minimum. A standard graduate course in each of real analysis, complex analysis, and functional analysis should be sufficient preparation for the reader Nota de contenido: Preface -- Chapter 1. Preliminaries -- Chapter 2. Fock Spaces -- Chapter 3. The Berezin Transform and BMO -- Chapter 4. Interpolating and Sampling Sequences -- Chapter 5. Zero Sets for Fock Spaces -- Chapter 6. Toeplitz Operators -- Chapter 7. Small Hankel Operators -- Chapter 8. Hankel Operators -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-8801-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32711 Ejemplares
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Título : Cycle Spaces of Flag Domains : A Complex Geometric Viewpoint Tipo de documento: documento electrónico Autores: Gregor Fels ; SpringerLink (Online service) ; Alan T. Huckleberry ; Joseph A. Wolf Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2006 Colección: Progress in Mathematics num. 245 Número de páginas: XX, 339 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4479-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebraic geometry Topological groups Lie Global analysis (Mathematics) Manifolds Functions of complex variables Differential Quantum physics Geometry Groups, Groups Several Complex Variables and Analytic Spaces Analysis on Physics Clasificación: 51 Matemáticas Resumen: This monograph, divided into four parts, presents a comprehensive treatment and systematic examination of cycle spaces of flag domains. Assuming only a basic familiarity with the concepts of Lie theory and geometry, this work presents a complete structure theory for these cycle spaces, as well as their applications to harmonic analysis and algebraic geometry. Key features: * Accessible to readers from a wide range of fields, with all the necessary background material provided for the nonspecialist * Many new results presented for the first time * Driven by numerous examples * The exposition is presented from the complex geometric viewpoint, but the methods, applications and much of the motivation also come from real and complex algebraic groups and their representations, as well as other areas of geometry * Comparisons with classical Barlet cycle spaces are given * Good bibliography and index Researchers and graduate students in differential geometry, complex analysis, harmonic analysis, representation theory, transformation groups, algebraic geometry, and areas of global geometric analysis will benefit from this work Nota de contenido: to Flag Domain Theory -- Structure of Complex Flag Manifolds -- Real Group Orbits -- Orbit Structure for Hermitian Symmetric Spaces -- Open Orbits -- The Cycle Space of a Flag Domain -- Cycle Spaces as Universal Domains -- Universal Domains -- B-Invariant Hypersurfaces in MZ -- Orbit Duality via Momentum Geometry -- Schubert Slices in the Context of Duality -- Analysis of the Boundary of U -- Invariant Kobayashi-Hyperbolic Stein Domains -- Cycle Spaces of Lower-Dimensional Orbits -- Examples -- Analytic and Geometric Consequences -- The Double Fibration Transform -- Variation of Hodge Structure -- Cycles in the K3 Period Domain -- The Full Cycle Space -- Combinatorics of Normal Bundles of Base Cycles -- Methods for Computing H1(C; O) -- Classification for Simple with rank En línea: http://dx.doi.org/10.1007/0-8176-4479-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34869 Cycle Spaces of Flag Domains : A Complex Geometric Viewpoint [documento electrónico] / Gregor Fels ; SpringerLink (Online service) ; Alan T. Huckleberry ; Joseph A. Wolf . - Boston, MA : Birkhäuser Boston, 2006 . - XX, 339 p : online resource. - (Progress in Mathematics; 245) .
ISBN : 978-0-8176-4479-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebraic geometry Topological groups Lie Global analysis (Mathematics) Manifolds Functions of complex variables Differential Quantum physics Geometry Groups, Groups Several Complex Variables and Analytic Spaces Analysis on Physics Clasificación: 51 Matemáticas Resumen: This monograph, divided into four parts, presents a comprehensive treatment and systematic examination of cycle spaces of flag domains. Assuming only a basic familiarity with the concepts of Lie theory and geometry, this work presents a complete structure theory for these cycle spaces, as well as their applications to harmonic analysis and algebraic geometry. Key features: * Accessible to readers from a wide range of fields, with all the necessary background material provided for the nonspecialist * Many new results presented for the first time * Driven by numerous examples * The exposition is presented from the complex geometric viewpoint, but the methods, applications and much of the motivation also come from real and complex algebraic groups and their representations, as well as other areas of geometry * Comparisons with classical Barlet cycle spaces are given * Good bibliography and index Researchers and graduate students in differential geometry, complex analysis, harmonic analysis, representation theory, transformation groups, algebraic geometry, and areas of global geometric analysis will benefit from this work Nota de contenido: to Flag Domain Theory -- Structure of Complex Flag Manifolds -- Real Group Orbits -- Orbit Structure for Hermitian Symmetric Spaces -- Open Orbits -- The Cycle Space of a Flag Domain -- Cycle Spaces as Universal Domains -- Universal Domains -- B-Invariant Hypersurfaces in MZ -- Orbit Duality via Momentum Geometry -- Schubert Slices in the Context of Duality -- Analysis of the Boundary of U -- Invariant Kobayashi-Hyperbolic Stein Domains -- Cycle Spaces of Lower-Dimensional Orbits -- Examples -- Analytic and Geometric Consequences -- The Double Fibration Transform -- Variation of Hodge Structure -- Cycles in the K3 Period Domain -- The Full Cycle Space -- Combinatorics of Normal Bundles of Base Cycles -- Methods for Computing H1(C; O) -- Classification for Simple with rank En línea: http://dx.doi.org/10.1007/0-8176-4479-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34869 Ejemplares
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Título : Lie Theory : Harmonic Analysis on Symmetric Spaces—General Plancherel Theorems Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Jean-Philippe Anker ; Bent Orsted Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Colección: Progress in Mathematics num. 230 Número de páginas: VIII, 175 p. 3 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4426-0 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Topological groups Lie Harmonic analysis Functions of complex variables Differential geometry Groups, Groups Abstract Analysis Geometry Several Complex Variables and Analytic Spaces Theory Generalizations Clasificación: 51 Matemáticas Resumen: Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory. Harmonic Analysis on Symmetric Spaces—General Plancherel Theorems presents extensive surveys by E.P. van den Ban, H. Schlichtkrull, and P. Delorme of the spectacular progress over the past decade in deriving the Plancherel theorem on reductive symmetric spaces. Van den Ban’s introductory chapter explains the basic setup of a reductive symmetric space along with a careful study of the structure theory, particularly for the ring of invariant differential operators for the relevant class of parabolic subgroups. Advanced topics for the formulation and understanding of the proof are covered, including Eisenstein integrals, regularity theorems, Maass–Selberg relations, and residue calculus for root systems. Schlichtkrull provides a cogent account of the basic ingredients in the harmonic analysis on a symmetric space through the explanation and definition of the Paley–Wiener theorem. Approaching the Plancherel theorem through an alternative viewpoint, the Schwartz space, Delorme bases his discussion and proof on asymptotic expansions of eigenfunctions and the theory of intertwining integrals. Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, possibly even mathematical cosmology, Harmonic Analysis on Symmetric Spaces—General Plancherel Theorems provides a broad, clearly focused examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required Nota de contenido: The Plancherel Theorem for a Reductive Symmetric Space -- The Paley—Wiener Theorem for a Reductive Symmetric Space -- The Plancherel Formula on Reductive Symmetric Spaces from the Point of View of the Schwartz Space En línea: http://dx.doi.org/10.1007/b138865 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35183 Lie Theory : Harmonic Analysis on Symmetric Spaces—General Plancherel Theorems [documento electrónico] / SpringerLink (Online service) ; Jean-Philippe Anker ; Bent Orsted . - Boston, MA : Birkhäuser Boston, 2005 . - VIII, 175 p. 3 illus : online resource. - (Progress in Mathematics; 230) .
ISBN : 978-0-8176-4426-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Topological groups Lie Harmonic analysis Functions of complex variables Differential geometry Groups, Groups Abstract Analysis Geometry Several Complex Variables and Analytic Spaces Theory Generalizations Clasificación: 51 Matemáticas Resumen: Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory. Harmonic Analysis on Symmetric Spaces—General Plancherel Theorems presents extensive surveys by E.P. van den Ban, H. Schlichtkrull, and P. Delorme of the spectacular progress over the past decade in deriving the Plancherel theorem on reductive symmetric spaces. Van den Ban’s introductory chapter explains the basic setup of a reductive symmetric space along with a careful study of the structure theory, particularly for the ring of invariant differential operators for the relevant class of parabolic subgroups. Advanced topics for the formulation and understanding of the proof are covered, including Eisenstein integrals, regularity theorems, Maass–Selberg relations, and residue calculus for root systems. Schlichtkrull provides a cogent account of the basic ingredients in the harmonic analysis on a symmetric space through the explanation and definition of the Paley–Wiener theorem. Approaching the Plancherel theorem through an alternative viewpoint, the Schwartz space, Delorme bases his discussion and proof on asymptotic expansions of eigenfunctions and the theory of intertwining integrals. Well suited for both graduate students and researchers in semisimple Lie theory and neighboring fields, possibly even mathematical cosmology, Harmonic Analysis on Symmetric Spaces—General Plancherel Theorems provides a broad, clearly focused examination of semisimple Lie groups and their integral importance and applications to research in many branches of mathematics and physics. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups, symmetric spaces, and parabolic subgroups is required Nota de contenido: The Plancherel Theorem for a Reductive Symmetric Space -- The Paley—Wiener Theorem for a Reductive Symmetric Space -- The Plancherel Formula on Reductive Symmetric Spaces from the Point of View of the Schwartz Space En línea: http://dx.doi.org/10.1007/b138865 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35183 Ejemplares
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Título : Lie Theory : Unitary Representations and Compactifications of Symmetric Spaces Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Jean-Philippe Anker ; Bent Orsted Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Colección: Progress in Mathematics num. 229 Número de páginas: X, 207 p. 20 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4430-7 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Topological groups Lie Harmonic analysis Functions of complex variables Differential geometry Groups, Groups Geometry Several Complex Variables and Analytic Spaces Abstract Analysis Theory Generalizations Clasificación: 51 Matemáticas Resumen: Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory. Unitary Representations and Compactifications of Symmetric Spaces, a self-contained work by A. Borel, L. Ji, and T. Kobayashi, focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws for unitary representations, i.e., restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles. Ji's introductory chapter motivates the subject of symmetric spaces and their compactifications with carefully selected examples. A discussion of Satake and Furstenberg boundaries and a survey of the geometry of Riemannian symmetric spaces in general provide a good background for the second chapter, namely, the Borel–Ji authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Borel–Ji further examine constructions of Oshima, De Concini, Procesi, and Melrose, which demonstrate the wide applicability of compactification techniques. Kobayashi examines the important subject of branching laws. Important concepts from modern representation theory, such as Harish–Chandra modules, associated varieties, microlocal analysis, derived functor modules, and geometric quantization are introduced. Concrete examples and relevant exercises engage the reader. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups and symmetric spaces is required of the reader Nota de contenido: to Symmetric Spaces and Their Compactifications -- Compactifications of Symmetric and Locally Symmetric Spaces -- Restrictions of Unitary Representations of Real Reductive Groups En línea: http://dx.doi.org/10.1007/b139076 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35186 Lie Theory : Unitary Representations and Compactifications of Symmetric Spaces [documento electrónico] / SpringerLink (Online service) ; Jean-Philippe Anker ; Bent Orsted . - Boston, MA : Birkhäuser Boston, 2005 . - X, 207 p. 20 illus : online resource. - (Progress in Mathematics; 229) .
ISBN : 978-0-8176-4430-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Topological groups Lie Harmonic analysis Functions of complex variables Differential geometry Groups, Groups Geometry Several Complex Variables and Analytic Spaces Abstract Analysis Theory Generalizations Clasificación: 51 Matemáticas Resumen: Semisimple Lie groups, and their algebraic analogues over fields other than the reals, are of fundamental importance in geometry, analysis, and mathematical physics. Three independent, self-contained volumes, under the general title Lie Theory, feature survey work and original results by well-established researchers in key areas of semisimple Lie theory. Unitary Representations and Compactifications of Symmetric Spaces, a self-contained work by A. Borel, L. Ji, and T. Kobayashi, focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws for unitary representations, i.e., restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles. Ji's introductory chapter motivates the subject of symmetric spaces and their compactifications with carefully selected examples. A discussion of Satake and Furstenberg boundaries and a survey of the geometry of Riemannian symmetric spaces in general provide a good background for the second chapter, namely, the Borel–Ji authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Borel–Ji further examine constructions of Oshima, De Concini, Procesi, and Melrose, which demonstrate the wide applicability of compactification techniques. Kobayashi examines the important subject of branching laws. Important concepts from modern representation theory, such as Harish–Chandra modules, associated varieties, microlocal analysis, derived functor modules, and geometric quantization are introduced. Concrete examples and relevant exercises engage the reader. Knowledge of basic representation theory of Lie groups as well as familiarity with semisimple Lie groups and symmetric spaces is required of the reader Nota de contenido: to Symmetric Spaces and Their Compactifications -- Compactifications of Symmetric and Locally Symmetric Spaces -- Restrictions of Unitary Representations of Real Reductive Groups En línea: http://dx.doi.org/10.1007/b139076 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35186 Ejemplares
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