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One Complex Variable from the Several Variable Point of View by Peter V. Dovbush at Abbey's Bookshop,
One Complex Variable from the Several Variable Point of View
— —
Peter V. Dovbush Steven G. Krantz (Washington University, St. Louis, Missouri, USA)

One Complex Variable from the Several Variable Point of View

Peter V. Dovbush,  Steven G. Krantz (Washington University, St. Louis, Missouri, USA)

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English
CRC Press
29 June 2025
Complex analysis, complex variables
Series: Textbooks in Mathematics
Traditionally speaking, those who study the function theory of one complex variable spend little or no time thinking about several complex variables. Conversely, experts in the function theory of several complex variables do not consider one complex variable. One complex variable is the inspiration and testing ground for several complex variables, and several complex variables are the natural generalization of one complex variable.

The authors’ thesis here is that these two subject areas have much in common. These subject areas can gain a lot by learning to communicate with each other. These two fields are logically connected, and each can be used to explain and put the other into context. This is the purpose of this book.

The point of view and the methodology of the two subject areas are quite different. One complex variable is an aspect of traditional hard analysis. Several complex variables are more like algebraic geometry and differential equations, with some differential geometry thrown in. The authors intend to create a marriage of the function theory of one complex variable and the function theory of several complex variables, leading to a new and productive dialogue between the two disciplines.

The hope is for this book to foster and develop this miscegenation in a manner that leads to new collaborations and developments. There is much fertile ground here, and this book aims to breathe new life into it.
By:   , , , ,
Imprint:   CRC Press
Country of Publication:   United Kingdom
Dimensions:   Height: 234mm,  Width: 156mm, 
Weight:   920g
ISBN:   9781041020141
ISBN 10:   1041020147
Series:   Textbooks in Mathematics
Pages:   400
Publication Date:  
Audience:   College/higher education ,  Primary
Format:   Hardback
Publisher's Status:   Active
1 Introduction 2 Complex numbers 3 The Cauchy-Riemann Equations 4 Convergent Power Series 5 Montel’s Theorem And its Applications 6 Boundary Behavior of Holomorphic Functions 7 Sokhotskii—Plemelj theorem 8 The Dirichlet Problem 9 The Ahlfors Map 10 Reproducing Kernels in Complex Analysis 11 Conformal mappings 12 Fundamental Solutions in Complex Analysis: The Cauchy Riemann Operator

Peter V. Dovbush Dr. habil., Associate Professor, in Moldova State University, Institute of Mathematics and Computer Science. He received his Ph.D. in Lomonosov Moscow State University in 1983 and Doctor of Sciences in 2003. He has published over over 50 scholarly articles. Steven G. Krantz is a Professor of Mathematics at Washington University in St. Louis. He has previously taught at UCLA, Princeton University, and Penn State University. He received his Ph.D. from Princeton University in 1974. Krantz has directed 20 Ph.D. students and 8 Masters students. He has published over 130 books and over 300 scholarly articles. He is the holder of the Chauvenet Prize and the Beckenbach Book Award and the Kemper Prize. He is a Fellow of the American Mathematical Society.

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