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Geometric Proofs of some Classical Results on Boundary Values for Analytic Functions

Published online by Cambridge University Press:  20 November 2018

Enrique Villamor
Enrique Villamor*
Affiliation:
Department of Mathematics, Florida International University Miami, Florida 33199 U.S.A.
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Abstract

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In this note we are going to give a geometric proof, using the method of the extremal metric, of the following result of Beurling. For any analytic function f(z) in the unit disc Δ of the plane with a bounded Dirichlet integral, the set E on the boundary of the unit disc where the nontangential limits of f(z) do not exist has logarithmic capacity zero. Also, using an unpublished result of Beurling, we will prove different results on boundary values for different classes of functions.

Keywords

30C45Areally mean p-valentextremal metriclogarithmic capacity
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 2 , 01 June 1994 , pp. 263 - 269
Copyright
Copyright © Canadian Mathematical Society 1994

References

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