Author : Laszlo Szekelyhidi
Publisher : World Scientific
Page : 247 pages
File Size : 41,2 MB
Release : 2014-03-19
Category : Mathematics
ISBN : 9814531731
This book provides a modern introduction to harmonic analysis and synthesis on topological groups. It serves as a guide to the abstract theory of Fourier transformation. For the first time, it presents a detailed account of the theory of classical harmonic analysis together with the recent developments in spectral analysis and synthesis.
Author : Tullio Ceccherini-Silberstein
Publisher : Cambridge University Press
Page : 589 pages
File Size : 36,34 MB
Release : 2018-06-21
Category : Mathematics
ISBN : 1107182336
A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.
Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
Page : 345 pages
File Size : 30,6 MB
Release : 2020-12-14
Category : Education
ISBN : 1470461277
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.
Author : Roger Godement
Publisher : Springer
Page : 535 pages
File Size : 43,27 MB
Release : 2015-04-30
Category : Mathematics
ISBN : 3319169076
Analysis Volume IV introduces the reader to functional analysis (integration, Hilbert spaces, harmonic analysis in group theory) and to the methods of the theory of modular functions (theta and L series, elliptic functions, use of the Lie algebra of SL2). As in volumes I to III, the inimitable style of the author is recognizable here too, not only because of his refusal to write in the compact style used nowadays in many textbooks. The first part (Integration), a wise combination of mathematics said to be `modern' and `classical', is universally useful whereas the second part leads the reader towards a very active and specialized field of research, with possibly broad generalizations.
Author : Anton Deitmar
Publisher : Springer
Page : 330 pages
File Size : 38,35 MB
Release : 2014-06-21
Category : 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.
Author : Valery V. Volchkov
Publisher : Springer
Page : 0 pages
File Size : 27,19 MB
Release : 2011-11-30
Category : Mathematics
ISBN : 9781447122838
The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years. There has been much progress in a number of problems concerning local - pects of spectral analysis and spectral synthesis on homogeneous spaces. The study oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic analysis, complex analysis, partial differential equations, integral geometry, appr- imation theory, and other branches of contemporary mathematics. The present book describes recent advances in this direction of research. Symmetric spaces and the Heisenberg group are an active ?eld of investigation at 2 the moment. The simplest examples of symmetric spaces, the classical 2-sphere S 2 and the hyperbolic plane H , play familiar roles in many areas in mathematics. The n Heisenberg groupH is a principal model for nilpotent groups, and results obtained n forH may suggest results that hold more generally for this important class of Lie groups. The purpose of this book is to develop harmonic analysis of mean periodic functions on the above spaces.
Author : Yitzhak Katznelson
Publisher :
Page : 292 pages
File Size : 50,29 MB
Release : 1968
Category : Harmonic analysis
ISBN :
Author : Gerald B. Folland
Publisher : CRC Press
Page : 317 pages
File Size : 33,14 MB
Release : 2016-02-03
Category : 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
Author : Donald B. Percival
Publisher : Cambridge University Press
Page : 616 pages
File Size : 49,42 MB
Release : 1993-06-03
Category : Mathematics
ISBN : 9780521435413
This book is an up-to-date introduction to univariate spectral analysis at the graduate level, which reflects a new scientific awareness of spectral complexity, as well as the widespread use of spectral analysis on digital computers with considerable computational power. The text provides theoretical and computational guidance on the available techniques, emphasizing those that work in practice. Spectral analysis finds extensive application in the analysis of data arising in many of the physical sciences, ranging from electrical engineering and physics to geophysics and oceanography. A valuable feature of the text is that many examples are given showing the application of spectral analysis to real data sets. Special emphasis is placed on the multitaper technique, because of its practical success in handling spectra with intricate structure, and its power to handle data with or without spectral lines. The text contains a large number of exercises, together with an extensive bibliography.
Author : Dinakar Ramakrishnan
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 37,50 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 1475730853
A modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasising harmonic analysis on topological groups. The main goal is to cover John Tates visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries -- technical prerequisites that are often foreign to the typical, more algebraically inclined number theorist. While most of the existing treatments of Tates thesis are somewhat terse and less than complete, the intent here is to be more leisurely, more comprehensive, and more comprehensible. While the choice of objects and methods is naturally guided by specific mathematical goals, the approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups. The text addresses students who have taken a year of graduate-level course in algebra, analysis, and topology. Moreover, the work will act as a good reference for working mathematicians interested in any of these fields.
