Overview
- Written by an established authority in harmonic analysis of several complex variables
- Develops the harmonic analysis of several complex variables from the first principles
- Includes copious examples, explanations, and an exhaustive bibliography
- Contains several figures which illustrate the geometric nature of the subject
- Exercise sets at the end of each chapter are especially useful for graduate level students
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
- Finsler geometry
- Monge-Ampere equation
- d-bar Neumann problem
- harmonic analysis
- several complex variables
- holomorphic function
- Poisson kernel
- admissible convergence
- Heisenberg group
- prolegomena
- Folland-Stein theorem
- Calderon-Zygmund theory
- Szego integral
- Paley-Wiener theorem
- reproducing kernels
- constructive kernels
- canonical kernels
- Bergman kernel
- Bergman metric
- Cauchy-Riemann equations
About this book
Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment;preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.
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Authors and Affiliations
Bibliographic Information
Book Title: Harmonic and Complex Analysis in Several Variables
Authors: Steven G. Krantz
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-63231-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-63229-2Published: 28 September 2017
Softcover ISBN: 978-3-319-87503-3Published: 11 August 2018
eBook ISBN: 978-3-319-63231-5Published: 20 September 2017
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XII, 424
Number of Illustrations: 17 b/w illustrations, 66 illustrations in colour
Topics: Abstract Harmonic Analysis, Functions of a Complex Variable