IJPAM: Volume 12, No. 4 (2004)

SEMIGROUPS OF HOLOMORPHIC MAPPINGS
ON THE UNIT DISK WITH A BOUNDARY
FIXED POINT

Mark Elin$^1$, David Shoikhet$^2$, Vladimir Volkovich$^3$
$^{1,2}$Department of Mathematics
ORT Braude College
P.O. Box 78, 21982 Karmiel, ISRAEL
$^1$e-mail: elin_mark@hotmail.com
$^2$e-mail: davs27@net.netvision.il.com
$^3$Department Computer Science
ORT Braude College
P.O. Box 78, 21982 Karmiel, ISRAEL
e-mail: zeev@actcom.co.il


Abstract.In this paper we describe the class of holomorphic generators of semigroups on the unit disk having boundary fixed point. In particular, we study the asymptotic behavior of semigroups of hyperbolic type. A classical problem of branching processes is to find conditions providing the convergence of exponential type. We give a geometrical solution of this problem in terms of the Robertson class of starlike functions with respect to a boundary point.

Received: January 28, 2004

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

Key Words and Phrases: semigroups, holomorphic generators, K\oenigs function, Robertson class of univalent functions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 12
Issue: 4