IJPAM: Volume 5, No. 3 (2003)

REPRESENTATIONS OF HOLOMORPHIC
GENERATORS AND DISTORTION THEOREMS
FOR SPIRALLIKE FUNCTIONS WITH RESPECT
TO A BOUNDARY POINT

David Shoikhet
Department of Mathematics
ORT Braude College
P.O.Box 78, Karmiel 21982, ISRAEL
e-mail: davs@tx.technion.ac.il


Abstract.In this paper we consider some classes of holomorphic generators of one-parameter semigroups of holomorphic self-mappings of the open unit disk, which have boundary fixed points. In particular, we establish an infinitesimal version of the Julia-Caratheodory Theorem. Further, we apply these results to the study of classes of spirallike functions with respect to a boundary point.

Received: February 12, 2003

AMS Subject Classification: 30C45, 47H10, 47H20

Key Words and Phrases: one-parameter semigroup, holomorphic generator, starlike function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2003
Volume: 5
Issue: 3