Harmonic Analysis in Phase Space. (AM-122), Volume 122

Harmonic Analysis in Phase Space. (AM-122), Volume 122
Author: Gerald B. Folland
Publisher: Princeton University Press
Total Pages: 288
Release: 2016-03-02
Genre: Mathematics
ISBN: 1400882427

This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.

Harmonic Analysis in Phase Space

Harmonic Analysis in Phase Space
Author: G. B. Folland
Publisher: Princeton University Press
Total Pages: 292
Release: 1989-03-21
Genre: Mathematics
ISBN: 9780691085289

This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.

Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group

Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group
Author: Valery V. Volchkov
Publisher: Springer Science & Business Media
Total Pages: 667
Release: 2009-06-13
Genre: Mathematics
ISBN: 1848825331

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.

Sub-Riemannian Geometry

Sub-Riemannian Geometry
Author: Ovidiu Calin
Publisher: Cambridge University Press
Total Pages: 371
Release: 2009-04-20
Genre: Mathematics
ISBN: 0521897300

A comprehensive text and reference on sub-Riemannian and Heisenberg manifolds using a novel and robust variational approach.

Wavelet Theory and Its Applications

Wavelet Theory and Its Applications
Author: Randy K. Young
Publisher: Springer Science & Business Media
Total Pages: 233
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1461535840

The continuous wavelet transform has deep mathematical roots in the work of Alberto P. Calderon. His seminal paper on complex method of interpolation and intermediate spaces provided the main tool for describing function spaces and their approximation properties. The Calderon identities allow one to give integral representations of many natural operators by using simple pieces of such operators, which are more suited for analysis. These pieces, which are essentially spectral projections, can be chosen in clever ways and have proved to be of tremendous utility in various problems of numerical analysis, multidimensional signal processing, video data compression, and reconstruction of high resolution images and high quality speech. A proliferation of research papers and a couple of books, written in English (there is an earlier book written in French), have emerged on the subject. These books, so far, are written by specialists for specialists, with a heavy mathematical flavor, which is characteristic of the Calderon-Zygmund theory and related research of Duffin-Schaeffer, Daubechies, Grossman, Meyer, Morlet, Chui, and others. Randy Young's monograph is geared more towards practitioners and even non-specialists, who want and, probably, should be cognizant of the exciting proven as well as potential benefits which have either already emerged or are likely to emerge from wavelet theory.

Time-Frequency Analysis of Operators

Time-Frequency Analysis of Operators
Author: Elena Cordero
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 458
Release: 2020-09-21
Genre: Mathematics
ISBN: 311053245X

This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to study dispersive equations such as the Schrödinger, wave, and heat equations and related Strichartz problems. The first part of the book is addressed to non-experts, presenting the basics of time-frequency analysis: short time Fourier transform, Wigner distribution and other representations, function spaces and frames theory, and it can be read independently as a short text-book on this topic from graduate and under-graduate students, or scholars in other disciplines.

Nonlinearity

Nonlinearity
Author:
Publisher:
Total Pages: 850
Release: 2009-04
Genre: Mathematical analysis
ISBN:

Pseudo-Differential Operators

Pseudo-Differential Operators
Author: Hans G. Feichtinger
Publisher: Springer
Total Pages: 235
Release: 2008-08-15
Genre: Mathematics
ISBN: 3540682686

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hörmander in the sixties of the last century. Beside applications in the general theory of partial differential equations, they have their roots also in the study of quantization first envisaged by Hermann Weyl thirty years earlier. Thanks to the understanding of the connections of wavelets with other branches of mathematical analysis, quantum physics and engineering, such operators have been used under different names as mathematical models in signal analysis since the last decade of the last century. The volume investigates the mathematics of quantization and signals in the context of pseudo-differential operators, Weyl transforms, Daubechies operators, Wick quantization and time-frequency localization operators. Applications to quantization, signal analysis and the modern theory of PDE are highlighted.