Three Problems in Function Theory
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.
KeywordsApproximation 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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