Lectures on Harmonic Analysis / Edition 1

Lectures on Harmonic Analysis / Edition 1

by Thomas H. Wolff
     
 

ISBN-10: 0821834495

ISBN-13: 9780821834497

Pub. Date: 01/28/2003

Publisher: American Mathematical Society

This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform,

Overview

This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for further reading and research. Technicalities are kept to a minimum, and simpler but more basic methods are often favored over the most recent methods. The clear style of the exposition and the quick progression from fundamentals to advanced topics ensures that both graduate students and research mathematicians will benefit from the book.

Product Details

ISBN-13:
9780821834497
Publisher:
American Mathematical Society
Publication date:
01/28/2003
Series:
University Lecture Series, #29
Edition description:
New Edition
Pages:
137
Product dimensions:
10.24(w) x 7.09(h) x (d)

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