A Course in Abstract Harmonic Analysis (Paperback)

Gerald B. Folland

ISBN 10: 1032922214 / ISBN 13: 9781032922218

Verlag: Taylor & Francis Ltd, 2024

Beschreibung

Paperback. 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 Kacs simple proof of a restricted form of Wieners 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 entree to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form. This book presents the essentials of harmonic analysis on locally compact groups in a concise and accessible form. The text provides necessary background on Banach algebras and spectral theory, develops the theory of analysis on Abelian groups and compact groups, examines the theory of induced representations, and explores the theory of represen Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Bestandsnummer des Verkäufers 9781032922218

Bibliografische Details

• Titel: A Course in Abstract Harmonic Analysis (Paperback)
• Verlag: Taylor & Francis Ltd
• Veröffentlichungsdatum: 2024
• Sprache: Englisch
• ISBN-10: 1032922214
• ISBN-13: 9781032922218
• Bindung: Paperback
• Ausgabe: 2. Auflage
• Zustand: new

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den 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.