Approximation, Complex Analysis, and Potential Theory / Edition 1

by Norair Arakelian, Gert Sabidussi, Paul M. Gauthier

Overview

Hermann Weyl considered value distribution theory to be the greatest mathematical achievement of the first half of the 20th century. The present lectures show that this beautiful theory is still growing. An important tool is complex approximation and some of the lectures are devoted to this topic. Harmonic approximation started to flourish astonishingly rapidly towards the end of the 20th century, and the latest development, including approximation manifolds, are presented here.

Since de Branges confirmed the Bieberbach conjecture, the primary problem in geometric function theory is to find the precise value of the Bloch constant. After more than half a century without progress, a breakthrough was recently achieved and is presented. Other topics are also presented, including Jensen measures.

A valuable introduction to currently active areas of complex analysis and potential theory. Can be read with profit by both students of analysis and research mathematicians.

Product Details

ISBN-13:	9781402000294
Publisher:	Springer Netherlands
Publication date:	09/30/2001
Series:	NATO Science Series II: Mathematics, Physics and Chemistry , #37
Edition description:	2001
Pages:	264
Product dimensions:	6.30(w) x 9.45(h) x 0.02(d)

Table of Contents

Approximation and value distribution.- Uniform and tangential harmonic approximation.- Sobolev spaces and approximation problems for differential operators.- Holomorphic and harmonic approximation on Riemann surfaces.- On the Bloch constant.- Approximation of subharmonic functions with applications.- Harmonic approximation and its applications.- Jensen measures.- Simultaneous approximation in function spaces.