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A Course in Abstract Harmonic Analysis

  • Fester Einband
  • 320 Seiten
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Praise for the Previous Edition"This delightful book fills a long-standing gap in the literature on abstract harmonic analysis. ?... Weiterlesen
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Zusatztext Praise for the Previous Edition"This delightful book fills a long-standing gap in the literature on abstract harmonic analysis. ? To the reviewer's knowledge! no one existing book contains all of the topics that are treated in this one. ? [The author's] respect for the subject shows on every hand?through his careful writing style! which is concise! yet simple and elegant. The reviewer would encourage anyone with an interest in harmonic analysis to have this book in his or her personal library. ? a fine book that the reviewer would have been proud to write."-Robert S. Doran in Mathematical Reviews®! Issue 98c Informationen zum Autor Gerald B. Folland received his Ph.D in mathematics from Princeton University! New Jersey! USA in 1971. After two years at the Courant Institute of Mathematical Sciences! New York! USA! he joined the faculty of the University of Washington! Seattle! USA! where he is now professor emeritus of mathematics. He has written a number of research and expository articles on harmonic analysis and its applications! and he is the author of eleven textbooks and research monographs. Zusammenfassung A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis! this abstract theory creates a foundation for a great deal of modern analysis! and it contains a number of elegant results and techniques that are of interest in their own right. This book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary chapter containing the necessary background material on Banach algebras and spectral theory! the text sets out the general theory of locally compact groups and their unitary representations! followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive chapter on the theory of induced representations and its applications! and the book concludes with a more informal exposition on the theory of representations of non-Abelian! non-compact groups.Featuring extensive updates and new examples! the Second Edition:Adds a short section on von Neumann algebrasIncludes Mark Kac's simple proof of a restricted form of Wiener's theoremExplains the relation between SU(2) and SO(3) in terms of quaternions! an elegant method that brings SO(4) into the picture with little effortDiscusses representations of the discrete Heisenberg group and its central quotients! illustrating the Mackey machine for regular semi-direct products and the pathological phenomena for nonregular onesA Course in Abstract Harmonic Analysis! Second Edition serves as an entrée to advanced mathematics! presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form. Inhaltsverzeichnis Banach Algebras and Spectral TheoryBanach Algebras: Basic ConceptsGelfand TheoryNonunital Banach AlgebrasThe Spectral TheoremSpectral Theory of ?-RepresentationsVon Neumann AlgebrasNotes and ReferencesLocally Compact GroupsTopological GroupsHaar MeasureInterlude: Some TechnicalitiesThe Modular FunctionConvolutionsHomogeneous SpacesNotes and ReferencesBasic Representation TheoryUnitary RepresentationsRepresentations of a Group and Its Group AlgebraFunctions of Positive TypeNotes and ReferencesAnalysis on Locally Compact Abelian GroupsThe Dual GroupThe Fourier TransformThe Pontrjagin Duality TheoremRepresentations of Locally Compact Abelian GroupsClosed Ideals in L1(G)Spectral SynthesisThe Bohr CompactificationNotes and ReferencesAnalysis on Compact GroupsRepresentations of Compact GroupsThe Peter-Weyl TheoremFourier Analysis on Compact GroupsExamplesNotes and ReferencesInduced RepresentationsThe Inducing Constr...

Praise for the Previous Edition "This delightful book fills a long-standing gap in the literature on abstract harmonic analysis. To the reviewer's knowledge, no one existing book contains all of the topics that are treated in this one. [The author's] respect for the subject shows on every handthrough his careful writing style, which is concise, yet simple and elegant. The reviewer would encourage anyone with an interest in harmonic analysis to have this book in his or her personal library. a fine book that the reviewer would have been proud to write."Robert S. Doran in Mathematical Reviews®, Issue 98c

Autorentext
Gerald B. Folland received his Ph.D in mathematics from Princeton University, New Jersey, USA in 1971. After two years at the Courant Institute of Mathematical Sciences, New York, USA, he joined the faculty of the University of Washington, Seattle, USA, where he is now professor emeritus of mathematics. He has written a number of research and expository articles on harmonic analysis and its applications, and he is the author of eleven textbooks and research monographs.

Zusammenfassung
A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant results and techniques that are of interest in their own right. This book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary chapter containing the necessary background material on Banach algebras and spectral theory, the text sets out the general theory of locally compact groups and their unitary representations, followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive chapter on the theory of induced representations and its applications, and the book concludes with a more informal exposition on the theory of representations of non-Abelian, non-compact groups. Featuring extensive updates and new examples, the Second Edition: Adds a short section on von Neumann algebras Includes Mark Kac's simple proof of a restricted form of Wiener's theorem Explains the relation between SU(2) and SO(3) in terms of quaternions, an elegant method that brings SO(4) into the picture with little effort Discusses representations of the discrete Heisenberg group and its central quotients, illustrating the Mackey machine for regular semi-direct products and the pathological phenomena for nonregular ones A Course in Abstract Harmonic Analysis, Second Edition serves as an entrée to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.

Inhalt
Banach Algebras and Spectral TheoryBanach Algebras: Basic ConceptsGelfand TheoryNonunital Banach AlgebrasThe Spectral TheoremSpectral Theory of -RepresentationsVon Neumann AlgebrasNotes and References Locally Compact GroupsTopological GroupsHaar MeasureInterlude: Some TechnicalitiesThe Modular FunctionConvolutionsHomogeneous SpacesNotes and References Basic Representation TheoryUnitary RepresentationsRepresentations of a Group and Its Group AlgebraFunctions of Positive TypeNotes and References Analysis on Locally Compact Abelian GroupsThe Dual GroupThe Fourier TransformThe Pontrjagin Duality TheoremRepresentations of Locally Compact Abelian GroupsClosed Ideals in L1(G)Spectral SynthesisThe Bohr CompactificationNotes and References Analysis on Compact GroupsRepresentations of Compact GroupsThe Peter-Weyl TheoremFourier Analysis on Compact GroupsExamplesNotes and References Induced RepresentationsThe Inducing ConstructionThe Frobenius Reciprocity TheoremPseudomeasures and Induction in StagesSystems of ImprimitivityThe Imprimitivity TheoremIntroduction to the Mackey MachineExamples: The ClassicsMore Examples, Good and BadNotes and References Further Topics in Representation TheoryThe Group C* AlgebraThe Structure of the Dual SpaceTensor Products of RepresentationsDirect Integral DecompositionsThe Plancherel TheoremExamples AppendicesA Hilbert Space MiscellanyTrace-Class and Hilbert-Schmidt OperatorsTensor Products of Hilbert SpacesVector-Valued Integrals

Produktinformationen

Titel: A Course in Abstract Harmonic Analysis
Autor:
EAN: 9781498727136
ISBN: 1498727131
Format: Fester Einband
Herausgeber: CRC PR INC
Anzahl Seiten: 320
Gewicht: 660g
Größe: H241mm x B161mm x T25mm
Jahr: 2015
Auflage: Revised