Books in Fourier analysis

Fourier Series and Integrals

1st Edition
October 28, 1985
David Aldous + 3 more
English
Paperback
9 7 8 0 1 2 2 2 6 4 5 1 1

The ideas of Fourier have made their way into every branch of mathematics and mathematical physics, from the theory of numbers to quantum mechanics. Fourier Series and Integrals focuses on the extraordinary power and flexibility of Fourier's basic series and integrals and on the astonishing variety of applications in which it is the chief tool. It presents a mathematical account of Fourier ideas on the circle and the line, on finite commutative groups, and on a few important noncommutative groups. A wide variety of exercises are placed in nearly every section as an integral part of the text.

Recent Progress in Fourier Analysis

1st Edition
Volume 111
January 1, 1985
I. Peral + 1 more
English
eBook
9 7 8 0 0 8 0 8 7 2 2 2 3

Mathematical Methods for Wave Phenomena

1st Edition
July 27, 1984
Norman Bleistein
English
eBook
9 7 8 0 0 8 0 9 1 6 9 5 8

Computer Science and Applied Mathematics: Mathematical Methods for Wave Phenomena focuses on the methods of applied mathematics, including equations, wave fronts, boundary value problems, and scattering problems. The publication initially ponders on first-order partial differential equations, Dirac delta function, Fourier transforms, asymptotics, and second-order partial differential equations. Discussions focus on prototype second-order equations, asymptotic expansions, asymptotic expansions of Fourier integrals with monotonic phase, method of stationary phase, propagation of wave fronts, and variable index of refraction. The text then examines wave equation in one space dimension, as well as initial boundary value problems, characteristics for the wave equation in one space dimension, and asymptotic solution of the Klein-Gordon equation. The manuscript offers information on wave equation in two and three dimensions and Helmholtz equation and other elliptic equations. Topics include energy integral, domain of dependence, and uniqueness, scattering problems, Green's functions, and problems in unbounded domains and the Sommerfeld radiation condition. The asymptotic techniques for direct scattering problems and the inverse methods for reflector imaging are also elaborated. The text is a dependable reference for computer science experts and mathematicians pursuing studies on the mathematical methods of wave phenomena.

Mathematical Methods for Wave Phenomena

1st Edition
July 27, 1984
Norman Bleistein
English
eBook
9 7 8 0 0 8 0 9 1 6 9 5 8

II: Fourier Analysis, Self-Adjointness

1st Edition
Volume 2
September 28, 1975
Michael Reed + 1 more
English
Hardback
9 7 8 0 1 2 5 8 5 0 0 2 5
eBook
9 7 8 0 0 8 0 9 2 5 3 7 0

This volume will serve several purposes: to provide an introduction for graduate students not previously acquainted with the material, to serve as a reference for mathematical physicists already working in the field, and to provide an introduction to various advanced topics which are difficult to understand in the literature. Not all the techniques and application are treated in the same depth. In general, we give a very thorough discussion of the mathematical techniques and applications in quatum mechanics, but provide only an introduction to the problems arising in quantum field theory, classical mechanics, and partial differential equations. Finally, some of the material developed in this volume will not find applications until Volume III. For all these reasons, this volume contains a great variety of subject matter. To help the reader select which material is important for him, we have provided a "Reader's Guide" at the end of each chapter.

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Books in Fourier analysis

Fourier Series and Integrals

Recent Progress in Fourier Analysis

Mathematical Methods for Wave Phenomena

Mathematical Methods for Wave Phenomena

II: Fourier Analysis, Self-Adjointness