Commutative Harmonic Analysis III: Generalized Functions. Application

V. P. Havin, N. K. Nikol’skij (auth.), V. P. Havin, N. K. Nikol’skij (eds.)0387570349, 9780387570341

This EMS volume shows the great power provided by modern harmonic analysis, not only in mathematics, but also in mathematical physics and engineering. Aimed at a reader who has learned the principles of harmonic analysis, this book is intended to provide a variety of perspectives on this important classical subject. The authors have written an outstanding book which distinguishes itself by the authors’ excellent expository style.
It can be useful for the expert in one area of harmonic analysis who wishes to obtain broader knowledge of other aspects of the subject and also by graduate students in other areas of mathematics who wish a general but rigorous introduction to the subject.

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Table of contents :
Front Matter….Pages i-vii
Front Matter….Pages 1-2
Introduction….Pages 3-4
The Elementary Theory….Pages 5-14
The General Theory….Pages 15-38
The Fourier Transform….Pages 38-59
Special Problems….Pages 60-83
Contact Structures and Distributions….Pages 83-120
Front Matter….Pages 129-130
Introduction….Pages 131-135
The Optical Fourier Transform….Pages 136-147
Notes and Comments….Pages 147-159
Acoustic and Acousto-Optical Fourier Processors….Pages 160-173
Front Matter….Pages 177-179
Introduction….Pages 180-180
The Uncertainty Principle Without Complex Variables….Pages 181-207
Complex Methods….Pages 207-252
Back Matter….Pages 261-268