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Three Problems in Function Theory

  • J. E. Brennan
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 261)

Abstract

The three problems mentioned in the title are as follows: Lp-approximation by polynomials and rational functions; the uniqueness property of the analytic functions; and the integrability of the derivative in conformal mapping. The emphasis in this exposition is on potential theoretic ideas underlying many results presented.

Keywords

Approximation in the mean by polynomials crescent subnormal operator harmonic measure conformal map Dyn’kin extension theorem asymptotically holomorphic functions capacity 

Mathematics Subject Classification (2010)

Primary 30-02. Secondary 30E10 30C35 30C85 30D60 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of KentuckyLexingtonUSA

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