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Introduction to Fourier Analysis and Wavelets
 
Mark A. Pinsky Northwestern University, Evanston, IL
Front Cover for Introduction to Fourier Analysis and Wavelets
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Hardcover ISBN: 978-0-8218-4797-8
Product Code: GSM/102
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Electronic ISBN: 978-1-4704-1166-4
Product Code: GSM/102.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $58.40
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Front Cover for Introduction to Fourier Analysis and Wavelets
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  • Front Cover for Introduction to Fourier Analysis and Wavelets
  • Back Cover for Introduction to Fourier Analysis and Wavelets
Introduction to Fourier Analysis and Wavelets
Mark A. Pinsky Northwestern University, Evanston, IL
Available Formats:
Hardcover ISBN:  978-0-8218-4797-8
Product Code:  GSM/102
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $62.40
Electronic ISBN:  978-1-4704-1166-4
Product Code:  GSM/102.E
List Price: $73.00
MAA Member Price: $65.70
AMS Member Price: $58.40
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: $117.00
MAA Member Price: $105.30
AMS Member Price: $93.60
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 1022002; 376 pp
    MSC: Primary 42;

    This book provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. Necessary prerequisites to using the text are rudiments of the Lebesgue measure and integration on the real line. It begins with a thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem). Frequently, more than one proof is offered for a given theorem to illustrate the multiplicity of approaches.

    The second chapter treats the Fourier transform on Euclidean spaces, especially the author's results in the three-dimensional piecewise smooth case, which is distinct from the classical Gibbs–Wilbraham phenomenon of one-dimensional Fourier analysis. The Poisson summation formula treated in Chapter 3 provides an elegant connection between Fourier series on the circle and Fourier transforms on the real line, culminating in Landau's asymptotic formulas for lattice points on a large sphere.

    Much of modern harmonic analysis is concerned with the behavior of various linear operators on the Lebesgue spaces \(L^p(\mathbb{R}^n)\). Chapter 4 gives a gentle introduction to these results, using the Riesz–Thorin theorem and the Marcinkiewicz interpolation formula. One of the long-time users of Fourier analysis is probability theory. In Chapter 5 the central limit theorem, iterated log theorem, and Berry–Esseen theorems are developed using the suitable Fourier-analytic tools.

    The final chapter furnishes a gentle introduction to wavelet theory, depending only on the \(L_2\) theory of the Fourier transform (the Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis.

    The text contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.

    Originally published by Brooks Cole/Cengage Learning as ISBN: 978-0-534-37660-4.

    Readership

    Undergraduate and graduate students interested in Fourier transform and harmonic analysis.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Fourier series on the circle
    • Chapter 2. Fourier transforms on the line and space
    • Chapter 3. Fourier analysis in $L^p$ spaces
    • Chapter 4. Poisson simulation formula and multiple Fourier series
    • Chapter 5. Applications to probability theory
    • Chapter 6. Introduction to wavelets
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Volume: 1022002; 376 pp
MSC: Primary 42;

This book provides a concrete introduction to a number of topics in harmonic analysis, accessible at the early graduate level or, in some cases, at an upper undergraduate level. Necessary prerequisites to using the text are rudiments of the Lebesgue measure and integration on the real line. It begins with a thorough treatment of Fourier series on the circle and their applications to approximation theory, probability, and plane geometry (the isoperimetric theorem). Frequently, more than one proof is offered for a given theorem to illustrate the multiplicity of approaches.

The second chapter treats the Fourier transform on Euclidean spaces, especially the author's results in the three-dimensional piecewise smooth case, which is distinct from the classical Gibbs–Wilbraham phenomenon of one-dimensional Fourier analysis. The Poisson summation formula treated in Chapter 3 provides an elegant connection between Fourier series on the circle and Fourier transforms on the real line, culminating in Landau's asymptotic formulas for lattice points on a large sphere.

Much of modern harmonic analysis is concerned with the behavior of various linear operators on the Lebesgue spaces \(L^p(\mathbb{R}^n)\). Chapter 4 gives a gentle introduction to these results, using the Riesz–Thorin theorem and the Marcinkiewicz interpolation formula. One of the long-time users of Fourier analysis is probability theory. In Chapter 5 the central limit theorem, iterated log theorem, and Berry–Esseen theorems are developed using the suitable Fourier-analytic tools.

The final chapter furnishes a gentle introduction to wavelet theory, depending only on the \(L_2\) theory of the Fourier transform (the Plancherel theorem). The basic notions of scale and location parameters demonstrate the flexibility of the wavelet approach to harmonic analysis.

The text contains numerous examples and more than 200 exercises, each located in close proximity to the related theoretical material.

Originally published by Brooks Cole/Cengage Learning as ISBN: 978-0-534-37660-4.

Readership

Undergraduate and graduate students interested in Fourier transform and harmonic analysis.

  • Chapters
  • Chapter 1. Fourier series on the circle
  • Chapter 2. Fourier transforms on the line and space
  • Chapter 3. Fourier analysis in $L^p$ spaces
  • Chapter 4. Poisson simulation formula and multiple Fourier series
  • Chapter 5. Applications to probability theory
  • Chapter 6. Introduction to wavelets
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