UNIVALENT-FUNCTIONS AND THE POMPEIU PROBLEM

Authors
GAROFALO N SEGALA F
Citation
N. Garofalo et F. Segala, UNIVALENT-FUNCTIONS AND THE POMPEIU PROBLEM, Transactions of the American Mathematical Society, 346(1), 1994, pp. 137-146
Citations number
13
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Transactions of the American Mathematical Society → ACNP
ISSN journal
00029947
Volume
346
Issue
1
Year of publication
1994
Pages
137 - 146
Database
ISI
SICI code
0002-9947(1994)346:1<137:UATPP>2.0.ZU;2-8
Abstract
In this paper we prove a result on the Pompeiu problem. If the Schwarz function PSI of the boundary of a simply-connected domain OMEGA subse t-of R2 extends meromorphically into a certain portion E of OMEGA with a pole at some point z0 is-an-element-of E, then OMEGA has the Pompei u property unless PHI is a Mobius transformation, in which case OMEGA is a disk.