Arakelian / Gauthier Approximation, Complex Analysis, and Potential Theory

Erscheinungsjahr 2012
ISBN: 978-94-010-0979-9
Verlag: Springer Netherland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 37, 264 Seiten, eBook

Reihe: NATO Science Series II: Mathematics, Physics and Chemistry

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.

Zielgruppe

Research

Autoren/Hrsg.

Arakelian, Norair

Gauthier, Paul M.

Inhaltsverzeichnis

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.