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Dirichlet-finite outer functions

Part of: Miscellaneous topics of analysis in the complex domain Two-dimensional theory

Published online by Cambridge University Press:  09 April 2009

Shinji Yamashita
Shinji Yamashita
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Fukazawa, Setagaya, Tokyo 158, Japan
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Abstract

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Given a measurable function k non-negative a.e. on the circle |z| = 1, when is the outer function Tk (see(1.3)) continuous on the disk |z| < 1 and further, Dirichlet-finite: We shall show, among other results, that the answer is in the positive if , with ess inf k > 0.

MSC classification

Secondary: 30E20: Integration, integrals of Cauchy type, integral representations of analytic functions 30E25: Boundary value problems 31A10: Integral representations, integral operators, integral equations methods 31A20: Boundary behavior (theorems of Fatou type, etc.) 31A25: Boundary value and inverse problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 3 , October 1981 , pp. 289 - 293
Copyright
Copyright © Australian Mathematical Society 1981

References

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