Illinois Journal of Mathematics

A geometric problem in function theory

Henry Helson and Farhad Zabihi

Full-text: Open access

Abstract

The Riemann Mapping Theorem asserts that there is an analytic function in the unit disk taking its boundary values on any given simple smooth curve in the plane. A theorem of Szegö says that an analytic function in the disk can have boundary values lying on prescribed circles about the origin. We shall prove that the circles of Szegö's theorem can be replaced by other curves, giving a common generalization of these theorems.

Article information

Source
Illinois J. Math., Volume 51, Number 3 (2007), 1027-1034.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258131116

Digital Object Identifier
doi:10.1215/ijm/1258131116

Mathematical Reviews number (MathSciNet)
MR2379736

Zentralblatt MATH identifier
1151.30006

Subjects
Primary: 30C35: General theory of conformal mappings

Citation

Helson, Henry; Zabihi, Farhad. A geometric problem in function theory. Illinois J. Math. 51 (2007), no. 3, 1027--1034. doi:10.1215/ijm/1258131116. https://projecteuclid.org/euclid.ijm/1258131116


Export citation