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Explorations in Harmonic Analysis: With Applications to Complex Function Theory and the Heisenberg Group (Applied and Numerical Harmonic Analysis)

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Explorations in Harmonic Analysis: With Applications to Complex Function Theory and the Heisenberg Group (Applied and Numerical Harmonic Analysis) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This text introduces modern harmonic analysis in the context in which it is actually applied, in particular through complex function theory and partial differential equations. Topics progress from harmonic analysis to Fourier transform to Heisenberg analysis.

Synopsis:

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.

Table of Contents

Preface.- Background in Fourier Series.- The Fourier Transform.- Fractional and Singular Integrals.- Pseudodifferential Operators.- The Real Variable Point of View.- Several Complex Variables.- Canonical Integral Operators.- Boundary Behavior.- The Heisenberg Group.- Analysis on the Heisenberg Group.- Index.

Product Details

ISBN:
9780817646684
Author:
Krantz, Steven G.
Publisher:
Birkhauser
Location:
Boston, MA
Subject:
Mathematical Analysis
Subject:
Group Theory
Subject:
Differential Equations
Subject:
Harmonic analysis
Subject:
Fourier analysis
Subject:
Complex Function Theory
Subject:
Integral operators.
Subject:
Singular integrals.
Subject:
abstract harmonic analysis
Subject:
Approximations and Expansions
Subject:
Several Complex Variables and Analytic Spaces
Subject:
Group Theory and Generalizations
Subject:
PARTIAL DIFFERENTIAL EQUATIONS
Subject:
Mathematics-Analysis General
Subject:
Several Complex Variables and Analyti
Subject:
CSpaces
Subject:
Mathematics
Subject:
The Arts
Subject:
mathematics and statistics
Subject:
Differential equations, partial
Copyright:
Edition Description:
Book
Series:
Applied and Numerical Harmonic Analysis
Publication Date:
20090505
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
376
Dimensions:
235 x 155 mm 1560 gr

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History and Social Science » Politics » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Group Theory
Science and Mathematics » Mathematics » Harmonic Analysis

Explorations in Harmonic Analysis: With Applications to Complex Function Theory and the Heisenberg Group (Applied and Numerical Harmonic Analysis) New Hardcover
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Product details 376 pages Birkhauser Boston - English 9780817646684 Reviews:
"Synopsis" by , This text introduces modern harmonic analysis in the context in which it is actually applied, in particular through complex function theory and partial differential equations. Topics progress from harmonic analysis to Fourier transform to Heisenberg analysis.
"Synopsis" by , 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.
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