Equilibrium problems of potential theory in the complex plane

Andrei Martínez Finkelshtein

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

14 Scopus citations

Abstract

This is a short introduction to the theory of the logarithmic potential. in the complex plane. The central ideas are the concepts of energy and equilibrium. We prove some classical results characterizing the equilibrium distribution and discuss the extension of these notions to more general settings when an external field or constraints on the distribution are present. The tools provided by potential theory have a profound impact on different branches of analysis. We illustrate these applications with two examples from approximation theory and complex dynamics.

Original languageEnglish
Title of host publicationOrthogonal Polynomials and Special Functions
Subtitle of host publicationComputation and Applications
PublisherSpringer Verlag
Pages79-117
Number of pages39
ISBN (Print)3540310622, 9783540310624
DOIs
StatePublished - 1 Jan 2006
Externally publishedYes

Publication series

NameLecture Notes in Mathematics
Volume1883
ISSN (Print)0075-8434

ASJC Scopus subject areas

  • Algebra and Number Theory

Fingerprint

Dive into the research topics of 'Equilibrium problems of potential theory in the complex plane'. Together they form a unique fingerprint.

Cite this