Introduction to Abstract Harmonic Analysis
Introduction to Abstract Harmonic Analysis

Author: Lynn H. Loomis

Publisher: Courier Corporation

Published: 2011-06-01

Total Pages: 210

ISBN-13: 0486481239

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"Harmonic analysis is a branch of advanced mathematics with applications in such diverse areas as signal processing, medical imaging, and quantum mechanics. This classic monograph is the work of a prominent contributor to the field. Geared toward advanced undergraduates and graduate students, it focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition"--

A Course in Abstract Harmonic Analysis
A Course in Abstract Harmonic Analysis

Author: Gerald B. Folland

Publisher: CRC Press

Published: 2016-02-03

Total Pages: 317

ISBN-13: 1498727158

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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 resul

Principles of Harmonic Analysis
Principles of Harmonic Analysis

Author: Anton Deitmar

Publisher: Springer

Published: 2014-06-21

Total Pages: 330

ISBN-13: 3319057928

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This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.

Introduction to Abstract Harmonic Analysis
Introduction to Abstract Harmonic Analysis

Author: Lynn H. Loomis

Publisher: Courier Corporation

Published: 2013-05-09

Total Pages: 210

ISBN-13: 0486282317

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Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.

Abstract Harmonic Analysis of Continuous Wavelet Transforms
Abstract Harmonic Analysis of Continuous Wavelet Transforms

Author: Hartmut Führ

Publisher: Springer

Published: 2005-01-17

Total Pages: 207

ISBN-13: 3540315527

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This volume contains a systematic discussion of wavelet-type inversion formulae based on group representations, and their close connection to the Plancherel formula for locally compact groups. The connection is demonstrated by the discussion of a toy example, and then employed for two purposes: Mathematically, it serves as a powerful tool, yielding existence results and criteria for inversion formulae which generalize many of the known results. Moreover, the connection provides the starting point for a – reasonably self-contained – exposition of Plancherel theory. Therefore, the volume can also be read as a problem-driven introduction to the Plancherel formula.

Introduction to Harmonic Analysis and Generalized Gelfand Pairs
Introduction to Harmonic Analysis and Generalized Gelfand Pairs

Author: Gerrit van Dijk

Publisher: Walter de Gruyter

Published: 2009-12-23

Total Pages: 234

ISBN-13: 3110220202

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This book is intended as an introduction to harmonic analysis and generalized Gelfand pairs. Starting with the elementary theory of Fourier series and Fourier integrals, the author proceeds to abstract harmonic analysis on locally compact abelian groups and Gelfand pairs. Finally a more advanced theory of generalized Gelfand pairs is developed. This book is aimed at advanced undergraduates or beginning graduate students. The scope of the book is limited, with the aim of enabling students to reach a level suitable for starting PhD research. The main prerequisites for the book are elementary real, complex and functional analysis. In the later chapters, familiarity with some more advanced functional analysis is assumed, in particular with the spectral theory of (unbounded) self-adjoint operators on a Hilbert space. From the contents Fourier series Fourier integrals Locally compact groups Haar measures Harmonic analysis on locally compact abelian groups Theory and examples of Gelfand pairs Theory and examples of generalized Gelfand pairs

Introduction to the Representation Theory of Compact and Locally Compact Groups
Introduction to the Representation Theory of Compact and Locally Compact Groups

Author: Alain Robert

Publisher: Cambridge University Press

Published: 1983-02-10

Total Pages: 217

ISBN-13: 0521289750

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Because of their significance in physics and chemistry, representation of Lie groups has been an area of intensive study by physicists and chemists, as well as mathematicians. This introduction is designed for graduate students who have some knowledge of finite groups and general topology, but is otherwise self-contained. The author gives direct and concise proofs of all results yet avoids the heavy machinery of functional analysis. Moreover, representative examples are treated in some detail.

Harmonic Analysis on the Heisenberg Group
Harmonic Analysis on the Heisenberg Group

Author: Sundaram Thangavelu

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 204

ISBN-13: 1461217725

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The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable.