Softcover ISBN:  9781470451127 
Product Code:  CAR/27 
List Price:  $75.00 
MAA Member Price:  $56.25 
AMS Member Price:  $56.25 
eBook ISBN:  9781614440260 
Product Code:  CAR/27.E 
List Price:  $70.00 
MAA Member Price:  $52.50 
AMS Member Price:  $52.50 
Softcover ISBN:  9781470451127 
eBook: ISBN:  9781614440260 
Product Code:  CAR/27.B 
List Price:  $145.00 $110.00 
MAA Member Price:  $108.75 $82.50 
AMS Member Price:  $108.75 $82.50 
Softcover ISBN:  9781470451127 
Product Code:  CAR/27 
List Price:  $75.00 
MAA Member Price:  $56.25 
AMS Member Price:  $56.25 
eBook ISBN:  9781614440260 
Product Code:  CAR/27.E 
List Price:  $70.00 
MAA Member Price:  $52.50 
AMS Member Price:  $52.50 
Softcover ISBN:  9781470451127 
eBook ISBN:  9781614440260 
Product Code:  CAR/27.B 
List Price:  $145.00 $110.00 
MAA Member Price:  $108.75 $82.50 
AMS Member Price:  $108.75 $82.50 

Book DetailsThe Carus Mathematical MonographsVolume: 27; 1999; 357 pp
A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of waveletsone of the newest ideas in the subject.
A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.

Table of Contents

Chapters

Chapter 0. Overview of Measure Theory and Functional Analysis

Chapter 1. Fourier Series Basics

Chapter 2. The Fourier Transform

Chapter 3. Multiple Fourier Series

Chapter 4. Spherical Harmonics

Chapter 5. Fractional Integrals, Singular Integrals, and Hardy Spaces

Chapter 6. Modern Theories of Integral Operators

Chapter 7. Wavelets

Chapter 8. A Retrospective


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A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of waveletsone of the newest ideas in the subject.
A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.

Chapters

Chapter 0. Overview of Measure Theory and Functional Analysis

Chapter 1. Fourier Series Basics

Chapter 2. The Fourier Transform

Chapter 3. Multiple Fourier Series

Chapter 4. Spherical Harmonics

Chapter 5. Fractional Integrals, Singular Integrals, and Hardy Spaces

Chapter 6. Modern Theories of Integral Operators

Chapter 7. Wavelets

Chapter 8. A Retrospective