1647936756  

Explorations in Harmonic Analysis : with Applications to Complex Function Theory and the Heisenberg Group / by Steven G.G. Krantz; edited by John J. Benedetto

Krantz, Steven G. *1951-* ; Benedetto, John J.

1

Englisch

Boston, MA : Birkhäuser Boston, 2009

Online-Ressource (digital)

Includes bibliographical references and index

Buchausg. u.d.T.: Krantz, Steven G. *1951-*: Explorations in harmonic analysis. - Boston, Mass. : Birkhäuser, 2009. - XIV, 360 S.

978-0-8176-4669-1

Weitere Ausgaben: 978-0-8176-4668-4 (Druckausgabe)

DOI: 10.1007/978-0-8176-4669-1

""Contents""; ""Preface""; ""1 Ontology and History of Real Analysis""; ""2 The Central Idea: The Hilbert Transform""; ""3 Essentials of the Fourier Transform""; ""4 Fractional and Singular Integrals""; ""5 A Crash Course in Several Complex Variables""; ""6 Pseudoconvexity and Domains of Holomorphy""; ""7 Canonical Complex Integral Operators""; ""8 Hardy Spaces Old and New""; ""9 Introduction to the Heisenberg Group""; ""10 Analysis on the Heisenberg Group""; ""11 A Coda on Domains of Finite Type""; ""Appendix 1: Rudiments of Fourier Series""; ""Appendix 2: The Fourier Transform""

""Appendix 3: Pseudodifferential Operators""""References""; ""Index""

*Harmonische Analyse

*Abstrakte harmonische Analysis

*Harmonische Analyse

*Abstrakte harmonische Analysis

*Differential equations, partial ; Mathematics ; Group theory ; Harmonic analysis ; Fourier analysis ; Approximation theory. ; Functions of complex variables. ; Mathematical models. ; Differential equations, partial ; Fourier analysis ; Group theory ; Harmonic analysis ; Mathematics

Klassifikation der Library of Congress: QA403-403.3 ; QA403

Dewey Dezimal-Klassifikation: 515.2433; ; 515.785;

Regensburger Verbund-Klassifikation: SK 450: SA-SP Mathematik / SK Monografien / Fourieranalyse und Integraltransformationen

Book Industry Communication: PBKD

bisacsh: MAT034000

Mathematics Subject Classification: *43-02

Mathematics Subject Classification: 32-XX

Mathematics Subject Classification: 42-XX

Mathematics Subject Classification: 44-XX

Mathematics Subject Classification: 43-XX

Ontology and History of Real Analysis -- The Central Idea: The Hilbert Transform -- Essentials of the Fourier Transform -- Fractional and Singular Integrals -- A Crash Course in Several Complex Variables -- Pseudoconvexity and Domains of Holomorphy -- Canonical Complex Integral Operators -- Hardy Spaces Old and New -- to the Heisenberg Group -- Analysis on the Heisenberg Group -- A Coda on Domains of Finite Type.

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.

https://zbmath.org/?q=an:1171.43001 [Zentralblatt MATH]

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https://doi.org/10.1007/978-0-8176-4669-1 [E-books (Springer)]