Harmonic and complex analysis in several variables

✍ Scribed by Krantz, Steven George

• Publisher: Springer
• Year: 2017
• Tongue: English
• Leaves: 429
• Series: Springer monographs in mathematics
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xii
Introduction and Review (Steven G. Krantz)....Pages 1-18
Boundary Behavior (Steven G. Krantz)....Pages 19-57
The Heisenberg Group (Steven G. Krantz)....Pages 59-88
Analysis on the Heisenberg Group (Steven G. Krantz)....Pages 89-113
Reproducing Kernels (Steven G. Krantz)....Pages 115-130
More on the Bergman and Szegő Kernels (Steven G. Krantz)....Pages 131-193
The Bergman Metric (Steven G. Krantz)....Pages 195-211
Further Geometric and Analytic Theory (Steven G. Krantz)....Pages 213-243
Additional Analytic Topics (Steven G. Krantz)....Pages 245-308
The Solution of the Inhomogeneous Cauchy–Riemann Equations (Steven G. Krantz)....Pages 309-394
A Few Miscellaneous Topics (Steven G. Krantz)....Pages 395-403
Back Matter ....Pages 405-424

✦ Subjects

Harmonic analysis;MATHEMATICS / Calculus;MATHEMATICS / Mathematical Analysis