An Introduction to Harmonic Analysis
Author : Yitzhak Katznelson
Publisher :
Page : 292 pages
File Size : 15,51 MB
Release : 1968
Category : Harmonic analysis
ISBN :
Introduction to Abstract Harmonic Analysis
Author : Lynn H. Loomis
Publisher : Courier Corporation
Page : 210 pages
File Size : 24,64 MB
Release : 2011-06-01
Category : Mathematics
ISBN : 0486481239
Book Description
"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"--
An Introduction to Harmonic Analysis on Semisimple Lie Groups
Author : V. S. Varadarajan
Publisher : Cambridge University Press
Page : 326 pages
File Size : 36,88 MB
Release : 1999-07-22
Category : Mathematics
ISBN : 9780521663625
Book Description
Now in paperback, this graduate-level textbook is an introduction to the representation theory of semi-simple Lie groups. As such, it will be suitable for research students in algebra and analysis, and for research mathematicians requiring a readable account of the topic. The author emphasizes the development of the central themes of the sunject in the context of special examples, without losing sight of its general flow and structure. The book concludes with appendices sketching some basic topics with a comprehensive guide to further reading.
Introduction to Harmonic Analysis and Generalized Gelfand Pairs
Author : Gerrit van Dijk
Publisher : Walter de Gruyter
Page : 234 pages
File Size : 40,62 MB
Release : 2009-12-23
Category : Mathematics
ISBN : 3110220202
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
Quantum Harmonic Analysis
Author : Maurice A. de Gosson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 247 pages
File Size : 23,27 MB
Release : 2021-07-05
Category : Mathematics
ISBN : 3110722909
Book Description
Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.
Principles of Harmonic Analysis
Author : Anton Deitmar
Publisher : Springer
Page : 330 pages
File Size : 23,8 MB
Release : 2014-06-21
Category : Mathematics
ISBN : 3319057928
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.
Harmonic Analysis
Author : María Cristina Pereyra
Publisher : American Mathematical Soc.
Page : 437 pages
File Size : 19,58 MB
Release : 2012
Category : Mathematics
ISBN : 0821875663
Book Description
Conveys the remarkable beauty and applicability of the ideas that have grown from Fourier theory. It presents for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization).
Harmonic Analysis and Applications
Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 11,69 MB
Release : 2020-12-14
Category : Education
ISBN : 1470461277
Book Description
The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.
A First Course in Harmonic Analysis
Author : Anton Deitmar
Publisher : Springer Science & Business Media
Page : 154 pages
File Size : 19,91 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 147573834X
Book Description
This book introduces harmonic analysis at an undergraduate level. In doing so it covers Fourier analysis and paves the way for Poisson Summation Formula. Another central feature is that is makes the reader aware of the fact that both principal incarnations of Fourier theory, the Fourier series and the Fourier transform, are special cases of a more general theory arising in the context of locally compact abelian groups. The final goal of this book is to introduce the reader to the techniques used in harmonic analysis of noncommutative groups. These techniques are explained in the context of matrix groups as a principal example.
Discrete Harmonic Analysis
Author : Tullio Ceccherini-Silberstein
Publisher : Cambridge University Press
Page : 589 pages
File Size : 36,1 MB
Release : 2018-06-21
Category : Mathematics
ISBN : 1107182336
Book Description
A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.
