Introduction to Abstract Harmonic Analysis PDF Download

Author: Lynn H. Loomis
Publisher: Courier Corporation
ISBN: 0486282317
Category : Mathematics
Languages : en
Pages : 208

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Book Description
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.

Author: Gerald B. Folland
Publisher: CRC Press
ISBN: 1498727158
Category : Mathematics
Languages : en
Pages : 317

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Book Description
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

Author: Anton Deitmar
Publisher: Springer
ISBN: 3319057928
Category : Mathematics
Languages : en
Pages : 332

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Book Description
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.

Author: Yitzhak Katznelson
Publisher:
ISBN:
Category : Harmonic analysis
Languages : en
Pages : 292

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Book Description

Author: Hartmut Führ
Publisher: Springer
ISBN: 3540315527
Category : Mathematics
Languages : en
Pages : 193

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Book Description
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.

Author: Gerrit van Dijk
Publisher: Walter de Gruyter
ISBN: 3110220202
Category : Mathematics
Languages : en
Pages : 234

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Book Description
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

Author: H. Garth Dales
Publisher: Cambridge University Press
ISBN: 9780521535847
Category : Mathematics
Languages : en
Pages : 338

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Book Description
Table of contents

Author: Alain Robert
Publisher: Cambridge University Press
ISBN: 0521289750
Category : Mathematics
Languages : en
Pages : 217

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Book Description
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.

Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0817646698
Category : Mathematics
Languages : en
Pages : 362

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Book Description
This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.

Author: Christopher Heil
Publisher: Springer Science & Business Media
ISBN: 0817646868
Category : Mathematics
Languages : en
Pages : 549

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Book Description
This textbook is a self-contained introduction to the abstract theory of bases and redundant frame expansions and their use in both applied and classical harmonic analysis. The four parts of the text take the reader from classical functional analysis and basis theory to modern time-frequency and wavelet theory. Extensive exercises complement the text and provide opportunities for learning-by-doing, making the text suitable for graduate-level courses. The self-contained presentation with clear proofs is accessible to graduate students, pure and applied mathematicians, and engineers interested in the mathematical underpinnings of applications.