Traditional Fourier analysis, which has been remarkably effective
in many contexts, uses linear phase functions to study functions.
Some questions, such as problems involving arithmetic progressions,
naturally lead to the use of quadratic or higher order phases.
Higher order Fourier analysis is a subject that has become very
active only recently. Gowers, in groundbreaking work, developed
many of the basic concepts of this theory in order to give a new,
quantitative proof of Szemerédi's theorem on arithmetic
progressions. However, there are also precursors to this theory in
Weyl's classical theory of equidistribution, as well as in
Furstenberg's structural theory of dynamical systems. This book,
which is the first monograph in this area, aims to cover all of
these topics in a unified manner, as well as to survey some of the
most recent developments, such as the application of the theory to
count linear patterns in primes. The book serves as an introduction
to the field, giving the beginning graduate student in the subject
a high-level overview of the field. The text focuses on the
simplest illustrative examples of key results, serving as a
companion to the existing literature on the subject. There are
numerous exercises with which to test one's knowledge.
General
Imprint: |
American Mathematical Society
|
Country of origin: |
United States |
Series: |
Graduate Studies in Mathematics |
Release date: |
December 2012 |
Authors: |
Terence Tao
|
Dimensions: |
189 x 256 x 15mm (L x W x T) |
Format: |
Paperback
|
Pages: |
187 |
ISBN-13: |
978-1-4704-5998-7 |
Categories: |
Books
|
LSN: |
1-4704-5998-1 |
Barcode: |
9781470459987 |
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