Applied and Numerical Harmonic Analysis

Explorations in Harmonic Analysis

With Applications to Complex Function Theory and the Heisenberg Group

Authors: Krantz, Steven G

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  • Provides an introduction to a particular direction in modern harmonic analysis
  • Is a self-contained text on analysis of integral operators
  • Presents both fundamentals and applications of harmonic analysis, especially to important concepts about the Heisenberg group
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  • ISBN 978-0-8176-4669-1
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About this Textbook

This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.

Within the textbook, the new ideas on the Heisenberg group are applied to the study of estimates for both the Szegö and Poisson–Szegö integrals on the unit ball in complex space. Thus the main theme of the book is also tied into complex analysis of several variables. With a rigorous but well-paced exposition, this text provides all the necessary background in singular and fractional integrals, as well as Hardy spaces and the function theory of several complex variables, needed to understand Heisenberg analysis.

Explorations in Harmonic Analysis is ideal for graduate students in mathematics, physics, and engineering. Prerequisites include a fundamental background in real and complex analysis and some exposure to functional analysis.

Reviews

From the reviews:

“This is an ambitious introduction to a particular direction in modern harmonic analysis. It presents harmonic analysis in vitro – in a context in which it is actually applied complex variables and partial differential equations. This will make the learning experience more meaningful for graduate students who are just beginning to forge a path of research.” (Vasily A. Chernecky, Zentralblatt MATH, Vol. 1171, 2009)

“Writing a 350 page account on harmonic analysis … is no easy task and making the presentation suitable for graduate students even less so. … it is indeed the purpose of the book under review … . Krantz has done an admirable job in condensing the ideas of Stein’s tract into a highly readily text suitable for a wide variety of readers. … It is done with such an enthusiasm … that even seasoned mathematicians should be able to enjoy the book.” (Troels Roussau Johansen, Mathematical Reviews, Issue 2011 a)

“The text is very well organized: each chapter begins with an introductory Prologue, each section with a Capsule giving a quick preview of the material, and each key theorem is preceded by a Prelude providing motivation and putting the result in an adequate context. … The book will be useful for advanced courses on harmonic analysis, singular integrals, as well as reference text for researchers in various domains of analysis, both pure and applied.” (Gabriela Kohr, Studia Universitatis Babes-Bolyai, Mathematica, Vol. LV (4), December, 2010)


Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-0-8176-4669-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Hardcover $109.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Explorations in Harmonic Analysis
Book Subtitle
With Applications to Complex Function Theory and the Heisenberg Group
Authors
Series Title
Applied and Numerical Harmonic Analysis
Copyright
2009
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4669-1
DOI
10.1007/978-0-8176-4669-1
Hardcover ISBN
978-0-8176-4668-4
Series ISSN
2296-5009
Edition Number
1
Number of Pages
XIV, 362
Topics