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Título : Harmonic Analysis and Applications : In Honor of John J. Benedetto Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Heil, Christopher Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2006 Colección: Applied and Numerical Harmonic Analysis, ISSN 2296-5009 Número de páginas: XXX, 374 p. 13 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4504-5 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Approximation theory Fourier Functional Operator Abstract Analysis Theory Approximations and Expansions Clasificación: 51 Matemáticas Resumen: John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. This self-contained volume in honor of John covers a wide range of topics in harmonic analysis and related areas, including weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The invited chapters pay tribute to John’s many achievements and express an appreciation for both the mathematical and personal inspiration he has given to so many students, coauthors, and colleagues. Although the scope of the book is broad, chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected here are written by prominent, well-respected researchers and professionals in the field of harmonic analysis. The book is divided into the following five sections: * Classical harmonic analysis * Frame theory * Time-frequency analysis * Wavelet theory * Sampling theory and shift-invariant spaces Harmonic Analysis and Applications is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics. Contributors: A. Aldroubi, L. Baggett, G. Benke, C. Cabrelli, P.G. Casazza, O. Christensen, W. Czaja, M. Fickus, J.-P. Gabardo, K. Gröchenig, K. Guo, E. Hayashi, C. Heil, H.P. Heinig, J.A. Hogan, E. Kovacevic, D. Labate, J.D. Lakey, D. Larson, M.T. Leon, S. Li, W.-Q Lim, A. Lindner, U. Molter, A.M. Powell, B. Rom, E. Schulz, T. Sorrells, D. Speegle, K.F. Taylor, J.C. Tremain, D. Walnut, G. Weiss, E. Wilson, G. Zimmermann Nota de contenido: Harmonic Analysis -- The Gibbs Phenomenon in Higher Dimensions -- Weighted Sobolev Inequalities for Gradients -- Semidiscrete Multipliers -- Frame Theory -- A Physical Interpretation of Tight Frames -- Time-Frequency Analysis -- Recent Developments in the Balian-Low Theorem -- Some Problems Related to the Distributional Zak Transform -- Gabor Duality Characterizations -- A Pedestrian’s Approach to Pseudodifferential Operators -- Linear Independence of Finite Gabor Systems -- Wavelet Theory -- Explicit Cross-Sections of Singly Generated Group Actions -- The Theory of Wavelets with Composite Dilations -- Sampling Theory and Shift-Invariant Spaces -- Periodic Nonuniform Sampling in Shift-Invariant Spaces -- Sampling on Unions of Shifted Lattices in One Dimension -- Learning the Right Model from the Data -- Redundancy in the Frequency Domain -- Density Results for Frames of Exponentials En línea: http://dx.doi.org/10.1007/0-8176-4504-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34877 Harmonic Analysis and Applications : In Honor of John J. Benedetto [documento electrónico] / SpringerLink (Online service) ; Heil, Christopher . - Boston, MA : Birkhäuser Boston, 2006 . - XXX, 374 p. 13 illus : online resource. - (Applied and Numerical Harmonic Analysis, ISSN 2296-5009) .
ISBN : 978-0-8176-4504-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Approximation theory Fourier Functional Operator Abstract Analysis Theory Approximations and Expansions Clasificación: 51 Matemáticas Resumen: John J. Benedetto has had a profound influence not only on the direction of harmonic analysis and its applications, but also on the entire community of people involved in the field. This self-contained volume in honor of John covers a wide range of topics in harmonic analysis and related areas, including weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The invited chapters pay tribute to John’s many achievements and express an appreciation for both the mathematical and personal inspiration he has given to so many students, coauthors, and colleagues. Although the scope of the book is broad, chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected here are written by prominent, well-respected researchers and professionals in the field of harmonic analysis. The book is divided into the following five sections: * Classical harmonic analysis * Frame theory * Time-frequency analysis * Wavelet theory * Sampling theory and shift-invariant spaces Harmonic Analysis and Applications is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics. Contributors: A. Aldroubi, L. Baggett, G. Benke, C. Cabrelli, P.G. Casazza, O. Christensen, W. Czaja, M. Fickus, J.-P. Gabardo, K. Gröchenig, K. Guo, E. Hayashi, C. Heil, H.P. Heinig, J.A. Hogan, E. Kovacevic, D. Labate, J.D. Lakey, D. Larson, M.T. Leon, S. Li, W.-Q Lim, A. Lindner, U. Molter, A.M. Powell, B. Rom, E. Schulz, T. Sorrells, D. Speegle, K.F. Taylor, J.C. Tremain, D. Walnut, G. Weiss, E. Wilson, G. Zimmermann Nota de contenido: Harmonic Analysis -- The Gibbs Phenomenon in Higher Dimensions -- Weighted Sobolev Inequalities for Gradients -- Semidiscrete Multipliers -- Frame Theory -- A Physical Interpretation of Tight Frames -- Time-Frequency Analysis -- Recent Developments in the Balian-Low Theorem -- Some Problems Related to the Distributional Zak Transform -- Gabor Duality Characterizations -- A Pedestrian’s Approach to Pseudodifferential Operators -- Linear Independence of Finite Gabor Systems -- Wavelet Theory -- Explicit Cross-Sections of Singly Generated Group Actions -- The Theory of Wavelets with Composite Dilations -- Sampling Theory and Shift-Invariant Spaces -- Periodic Nonuniform Sampling in Shift-Invariant Spaces -- Sampling on Unions of Shifted Lattices in One Dimension -- Learning the Right Model from the Data -- Redundancy in the Frequency Domain -- Density Results for Frames of Exponentials En línea: http://dx.doi.org/10.1007/0-8176-4504-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34877 Ejemplares
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Título : Harmonic Analysis of Operators on Hilbert Space Tipo de documento: documento electrónico Autores: Sz.-Nagy, Béla ; SpringerLink (Online service) ; Foias, Ciprian ; Hari Bercovici ; Kérchy, László Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Colección: Universitext, ISSN 0172-5939 Número de páginas: XIV, 478 p. 1 illus Il.: online resource ISBN/ISSN/DL: 978-1-4419-6094-8 Idioma : Inglés (eng) Palabras clave: Mathematics Harmonic analysis Functional Functions of complex variables Operator theory a Complex Variable Analysis Abstract Theory Clasificación: 51 Matemáticas Resumen: The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory. Specifically, the last two chapters of the book continue and complete the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition Nota de contenido: Contractions and Their Dilations -- Geometrical and Spectral Properties of Dilations -- Functional Calculus -- Extended Functional Calculus -- Operator-Valued Analytic Functions -- Functional Models -- Regular Factorizations and Invariant Subspaces -- Weak Contractions -- The Structure of C1.-Contractions -- The Structure of Operators of Class C0 En línea: http://dx.doi.org/10.1007/978-1-4419-6094-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33626 Harmonic Analysis of Operators on Hilbert Space [documento electrónico] / Sz.-Nagy, Béla ; SpringerLink (Online service) ; Foias, Ciprian ; Hari Bercovici ; Kérchy, László . - New York, NY : Springer New York, 2010 . - XIV, 478 p. 1 illus : online resource. - (Universitext, ISSN 0172-5939) .
ISBN : 978-1-4419-6094-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Harmonic analysis Functional Functions of complex variables Operator theory a Complex Variable Analysis Abstract Theory Clasificación: 51 Matemáticas Resumen: The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory. Specifically, the last two chapters of the book continue and complete the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition Nota de contenido: Contractions and Their Dilations -- Geometrical and Spectral Properties of Dilations -- Functional Calculus -- Extended Functional Calculus -- Operator-Valued Analytic Functions -- Functional Models -- Regular Factorizations and Invariant Subspaces -- Weak Contractions -- The Structure of C1.-Contractions -- The Structure of Operators of Class C0 En línea: http://dx.doi.org/10.1007/978-1-4419-6094-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33626 Ejemplares
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Título : Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane Tipo de documento: documento electrónico Autores: Terras, Audrey ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2013 Otro editor: Imprint: Springer Número de páginas: XVII, 413 p. 83 illus., 32 illus. in color Il.: online resource ISBN/ISSN/DL: 978-1-4614-7972-7 Idioma : Inglés (eng) Palabras clave: Mathematics Group theory Topological groups Lie Harmonic analysis Fourier Functions of complex variables Special functions Abstract Analysis Theory and Generalizations Groups, Groups a Complex Variable Clasificación: 51 Matemáticas Resumen: This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections, new topics, and updates have been incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maass waveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups G, tessellations of H from such discrete group actions, automorphic forms, the Selberg trace formula and its applications in spectral theory as well as number theory Nota de contenido: Chapter 1 Flat Space. Fourier Analysis on R^m. -- 1.1 Distributions or Generalized Functions -- 1.2 Fourier Integrals -- 1.3 Fourier Series and the Poisson Summation Formula -- 1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions -- 1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyl’s Criterion for Uniform Distribution -- Chapter 2 A Compact Symmetric Space--The Sphere -- 2.1 Fourier Analysis on the Sphere -- 2.2 O(3) and R^3. The Radon Transform -- Chapter 3 The Poincaré Upper Half-Plane -- 3.1 Hyperbolic Geometry -- 3.2 Harmonic Analysis on H -- 3.3 Fundamental Domains for Discrete Subgroups G of G = SL(2, R) -- 3.4 Modular of Automorphic Forms--Classical -- 3.5 Automorphic Forms--Not So Classical--Maass Waveforms -- 3.6 Modular Forms and Dirichlet Series. Hecke Theory and Generalizations -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-7972-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32374 Harmonic Analysis on Symmetric Spaces—Euclidean Space, the Sphere, and the Poincaré Upper Half-Plane [documento electrónico] / Terras, Audrey ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2013 . - XVII, 413 p. 83 illus., 32 illus. in color : online resource.
ISBN : 978-1-4614-7972-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Group theory Topological groups Lie Harmonic analysis Fourier Functions of complex variables Special functions Abstract Analysis Theory and Generalizations Groups, Groups a Complex Variable Clasificación: 51 Matemáticas Resumen: This unique text is an introduction to harmonic analysis on the simplest symmetric spaces, namely Euclidean space, the sphere, and the Poincaré upper half plane. This book is intended for beginning graduate students in mathematics or researchers in physics or engineering. Written with an informal style, the book places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering. Many corrections, new topics, and updates have been incorporated in this new edition. These include discussions of the work of P. Sarnak and others making progress on various conjectures on modular forms, the work of T. Sunada, Marie-France Vignéras, Carolyn Gordon, and others on Mark Kac's question "Can you hear the shape of a drum?", Ramanujan graphs, wavelets, quasicrystals, modular knots, triangle and quaternion groups, computations of Maass waveforms, and, finally, the author's comparisons of continuous theory with the finite analogues. Topics featured throughout the text include inversion formulas for Fourier transforms, central limit theorems, Poisson's summation formula and applications in crystallography and number theory, applications of spherical harmonic analysis to the hydrogen atom, the Radon transform, non-Euclidean geometry on the Poincaré upper half plane H or unit disc and applications to microwave engineering, fundamental domains in H for discrete groups G, tessellations of H from such discrete group actions, automorphic forms, the Selberg trace formula and its applications in spectral theory as well as number theory Nota de contenido: Chapter 1 Flat Space. Fourier Analysis on R^m. -- 1.1 Distributions or Generalized Functions -- 1.2 Fourier Integrals -- 1.3 Fourier Series and the Poisson Summation Formula -- 1.4 Mellin Transforms, Epstein and Dedekind Zeta Functions -- 1.5 Finite Symmetric Spaces, Wavelets, Quasicrystals, Weyl’s Criterion for Uniform Distribution -- Chapter 2 A Compact Symmetric Space--The Sphere -- 2.1 Fourier Analysis on the Sphere -- 2.2 O(3) and R^3. The Radon Transform -- Chapter 3 The Poincaré Upper Half-Plane -- 3.1 Hyperbolic Geometry -- 3.2 Harmonic Analysis on H -- 3.3 Fundamental Domains for Discrete Subgroups G of G = SL(2, R) -- 3.4 Modular of Automorphic Forms--Classical -- 3.5 Automorphic Forms--Not So Classical--Maass Waveforms -- 3.6 Modular Forms and Dirichlet Series. Hecke Theory and Generalizations -- References -- Index En línea: http://dx.doi.org/10.1007/978-1-4614-7972-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32374 Ejemplares
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Título : Harmonic Analysis, Signal Processing, and Complexity : Festschrift in Honor of the 60th Birthday of Carlos A. Berenstein Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Sabadini, Irene ; Struppa, Daniele C ; Walnut, David F Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Colección: Progress in Mathematics num. 238 Número de páginas: XI, 162 p. 15 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4416-1 Idioma : Inglés (eng) Palabras clave: Mathematics Algorithms Mathematical analysis Analysis (Mathematics) Harmonic Applied mathematics Engineering Abstract Applications of Signal, Image and Speech Processing Algorithm Problem Complexity Clasificación: 51 Matemáticas Resumen: Carlos A. Berenstein has had a profound influence on scholars and practitioners alike amid a distinguished mathematical career spanning nearly four decades. His uncommon capability of adroitly moving between these parallel worlds is demonstrated by the breadth of his research interests, from his early theoretical work on interpolation in spaces of entire functions with growth conditions and residue theory to his later work on deconvolution and its applications to issues ranging from optics to the study of blood flow. This volume, which celebrates his sixtieth birthday, reflects the state-of-the-art in these areas. Original articles and survey articles, all refereed, cover topics in harmonic and complex analysis, as well as more applied work in signal processing. Contributors: C.A. Berenstein; R.W. Braun; O. Calin; D-C. Chang; G. Dafni; L. Ehrenpreis; G. Kaiser; C.O. Kiselman; P. Krishnaprasad; B.Q. Li; B. Matt; R. Meise; D. Napoletani; R. Poovendran; Y. Qiao; J. Ryan; C. Sadosky; D.C. Struppa; B.A. Taylor; J. Tie; D.F. Walnut; and A. Yger Nota de contenido: Some Novel Aspects of the Cauchy Problem -- Analytic and Algebraic Ideas: How to Profit from Their Complementarity -- On Certain First-Order Partial Differential Equations in C n -- Hermite Operator on the Heisenberg Group -- A Div-Curl Lemma in BMO on a Domain -- Subharmonic Functions on Discrete Structures -- Nearly Hyperbolic Varieties and Phragmén-Lindelöf Conditions -- Sampling and Local Deconvolution -- Orthogonal Projections on Hyperbolic Space -- Eigenwavelets of the Wave Equation -- Security Analysis and Extensions of the PCB Algorithm for Distributed Key Generation -- Quotient Signal Estimation En línea: http://dx.doi.org/10.1007/0-8176-4416-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35174 Harmonic Analysis, Signal Processing, and Complexity : Festschrift in Honor of the 60th Birthday of Carlos A. Berenstein [documento electrónico] / SpringerLink (Online service) ; Sabadini, Irene ; Struppa, Daniele C ; Walnut, David F . - Boston, MA : Birkhäuser Boston, 2005 . - XI, 162 p. 15 illus : online resource. - (Progress in Mathematics; 238) .
ISBN : 978-0-8176-4416-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Algorithms Mathematical analysis Analysis (Mathematics) Harmonic Applied mathematics Engineering Abstract Applications of Signal, Image and Speech Processing Algorithm Problem Complexity Clasificación: 51 Matemáticas Resumen: Carlos A. Berenstein has had a profound influence on scholars and practitioners alike amid a distinguished mathematical career spanning nearly four decades. His uncommon capability of adroitly moving between these parallel worlds is demonstrated by the breadth of his research interests, from his early theoretical work on interpolation in spaces of entire functions with growth conditions and residue theory to his later work on deconvolution and its applications to issues ranging from optics to the study of blood flow. This volume, which celebrates his sixtieth birthday, reflects the state-of-the-art in these areas. Original articles and survey articles, all refereed, cover topics in harmonic and complex analysis, as well as more applied work in signal processing. Contributors: C.A. Berenstein; R.W. Braun; O. Calin; D-C. Chang; G. Dafni; L. Ehrenpreis; G. Kaiser; C.O. Kiselman; P. Krishnaprasad; B.Q. Li; B. Matt; R. Meise; D. Napoletani; R. Poovendran; Y. Qiao; J. Ryan; C. Sadosky; D.C. Struppa; B.A. Taylor; J. Tie; D.F. Walnut; and A. Yger Nota de contenido: Some Novel Aspects of the Cauchy Problem -- Analytic and Algebraic Ideas: How to Profit from Their Complementarity -- On Certain First-Order Partial Differential Equations in C n -- Hermite Operator on the Heisenberg Group -- A Div-Curl Lemma in BMO on a Domain -- Subharmonic Functions on Discrete Structures -- Nearly Hyperbolic Varieties and Phragmén-Lindelöf Conditions -- Sampling and Local Deconvolution -- Orthogonal Projections on Hyperbolic Space -- Eigenwavelets of the Wave Equation -- Security Analysis and Extensions of the PCB Algorithm for Distributed Key Generation -- Quotient Signal Estimation En línea: http://dx.doi.org/10.1007/0-8176-4416-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35174 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 ; Orsted, Bent 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 ; Orsted, Bent . - 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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