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Higher Order Fourier Analysis
 
Terence Tao University of California, Los Angeles, Los Angeles, CA
Front Cover for Higher Order Fourier Analysis
Available Formats:
Softcover ISBN: 978-1-4704-5998-7
Product Code: GSM/142.S
187 pp 
List Price: $58.00
MAA Member Price: $52.20
AMS Member Price: $46.40
Electronic ISBN: 978-0-8218-9194-0
Product Code: GSM/142.E
187 pp 
List Price: $54.00
MAA Member Price: $48.60
AMS Member Price: $43.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $87.00
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Front Cover for Higher Order Fourier Analysis
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  • Front Cover for Higher Order Fourier Analysis
  • Back Cover for Higher Order Fourier Analysis
Higher Order Fourier Analysis
Terence Tao University of California, Los Angeles, Los Angeles, CA
Available Formats:
Softcover ISBN:  978-1-4704-5998-7
Product Code:  GSM/142.S
187 pp 
List Price: $58.00
MAA Member Price: $52.20
AMS Member Price: $46.40
Electronic ISBN:  978-0-8218-9194-0
Product Code:  GSM/142.E
187 pp 
List Price: $54.00
MAA Member Price: $48.60
AMS Member Price: $43.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $87.00
MAA Member Price: $78.30
AMS Member Price: $69.60
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1422012
    MSC: Primary 11; 37;

    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.

    Readership

    Graduate students and research mathematicians interested in harmonic analysis and number theory.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Higher order Fourier analysis
    • Chapter 2. Related articles
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Volume: 1422012
MSC: Primary 11; 37;

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.

Readership

Graduate students and research mathematicians interested in harmonic analysis and number theory.

  • Chapters
  • Chapter 1. Higher order Fourier analysis
  • Chapter 2. Related articles
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