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Handbook of Complex Analysis

Edited By

Steven G. Krantz



  • Available for pre-order. Item will ship after December 31, 2021
ISBN 9781138064041
December 31, 2021 Forthcoming by Chapman and Hall/CRC
456 Pages 22 B/W Illustrations

 
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Book Description

In spite of being nearly 500 years old, the subject of complex analysis is still today a vital and active part of mathematics. There are important applications in physics, engineering, and other aspects of technology.

This Handbook presents contributed chapters by several of prominent mathematicians, including the new generation of researchers. More though than a compilation of recent results, this book offers students an essential stepping-stone for students to gain an entry into the research life of complex analysis. Classes and seminars play a role in this process. More, though, is needed for further study. This Handbook will play that role.

This book is also a reference and a source of inspiration for more seasoned mathematicians—both specialists in complex analysis and others who want to acquaint themselves with current modes of thought.

The chapters in this volume are authored by leading experts in the field, also gifted expositors. They are carefully crafted presentations of diverse aspects of the field, formulate for a broad and diverse audience. The Editors intends this volume is a touchstone for current ideas in the broadly construed subject area of complex analysis. It should enrich the literature and point in some new directions.

Table of Contents

Preface
1.Something about poisson and dirichlet
2.The Cauchy-Leray operator for convex domains
3.Fractional linear maps and some applications. An “Augenblick”
4.Biholomorphic transformations
5.Positivity in the @-Neumann Problem
6.Symmetry and art
7.A glimpse into invariant distances in complex analysis
8.Variations on the (eternal) theme of analytic continuation
9.Complex convexity
10.Reproducing kernels in complex analysis
11.The Green’s function method on the Riemann mapping theorem
12.Polynomial trace identities in quaternion algebras and two-generator Kleinian groups
13.Boundary value problems on klein surfaces
Bibliography
Index     

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Editor(s)

Biography

Steven G. Krantz is a professor of mathematics at Washington University in St. Louis. He has previously taught at UCLA, Princeton University, and Pennsylvania State University. He has written more than 130 books and more than 250 scholarly papers and is the founding editor of the Journal of Geometric Analysis. An AMS Fellow, Dr. Krantz has been a recipient of the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize. He received a Ph.D. from Princeton University.