Introduction to Abstract Harmonic Analysis

Introduction to Abstract Harmonic Analysis
Author: Lynn H. Loomis
Publisher: Courier Corporation
Total Pages: 210
Release: 2011-06-01
Genre: Mathematics
ISBN: 0486481239

"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
Total Pages: 317
Release: 2016-02-03
Genre: Mathematics
ISBN: 1498727158

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
Total Pages: 330
Release: 2014-06-21
Genre: Mathematics
ISBN: 3319057928

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
Total Pages: 210
Release: 2013-05-09
Genre: Mathematics
ISBN: 0486282317

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
Total Pages: 207
Release: 2005-01-17
Genre: Mathematics
ISBN: 3540315527

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
Total Pages: 234
Release: 2009-12-23
Genre: Mathematics
ISBN: 3110220202

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
Total Pages: 217
Release: 1983-02-10
Genre: Mathematics
ISBN: 0521289750

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 and Applied Analysis

Harmonic and Applied Analysis
Author: Stephan Dahlke
Publisher: Birkhäuser
Total Pages: 268
Release: 2015-09-12
Genre: Mathematics
ISBN: 3319188631

This contributed volume explores the connection between the theoretical aspects of harmonic analysis and the construction of advanced multiscale representations that have emerged in signal and image processing. It highlights some of the most promising mathematical developments in harmonic analysis in the last decade brought about by the interplay among different areas of abstract and applied mathematics. This intertwining of ideas is considered starting from the theory of unitary group representations and leading to the construction of very efficient schemes for the analysis of multidimensional data. After an introductory chapter surveying the scientific significance of classical and more advanced multiscale methods, chapters cover such topics as An overview of Lie theory focused on common applications in signal analysis, including the wavelet representation of the affine group, the Schrödinger representation of the Heisenberg group, and the metaplectic representation of the symplectic group An introduction to coorbit theory and how it can be combined with the shearlet transform to establish shearlet coorbit spaces Microlocal properties of the shearlet transform and its ability to provide a precise geometric characterization of edges and interface boundaries in images and other multidimensional data Mathematical techniques to construct optimal data representations for a number of signal types, with a focus on the optimal approximation of functions governed by anisotropic singularities. A unified notation is used across all of the chapters to ensure consistency of the mathematical material presented. Harmonic and Applied Analysis: From Groups to Signals is aimed at graduate students and researchers in the areas of harmonic analysis and applied mathematics, as well as at other applied scientists interested in representations of multidimensional data. It can also be used as a textbook for graduate courses in applied harmonic analysis.​