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Computational Methods and Function Theory 5 (2005), No. 1, 223--235
Copyright Heldermann Verlag 2005

Covering Properties of Most Entire Functions on Stein Manifolds

Paul M. Gauthier
gauthier@dms.umontreal.ca , Département de mathématiques et de statistique, Université de Montréal, CP 6128 Centre Ville, Montréal, Québec H3C 3J7, Canada.

Mohamad R. Pouryayevali
pourya@sci.ui.ac.ir , Department of Mathematics, University of Isfahan, P. O. Box 81745-163, Isfahan, Iran.

[Abstract-pdf] [Abstract-ps]

On a Stein manifold, we obtain generic versions of two covering theorems of Valiron and Birkhoff respectively. Namely, we show that most equidimensional holomorphic mappings into complex Euclidean space contain arbitrarily large `schlicht' balls in their images. Moreover, most global holomorphic functions have a universality property which consists in approximately reproducing all local holomorphic functions.

Keywords: Universal functions, Bloch radius.

MSC 2000: Primary 32E30, 32Q28; Secondary 30E10, 30C25.

[FullText-pdf (259 K)] [FullText-ps (442 K)]