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ON THE RANGE OF UNIVERSAL FUNCTIONS

Published online by Cambridge University Press:  01 July 2000

G. COSTAKIS  and
A. MELAS
G. COSTAKIS
Affiliation:
Department of Mathematics, University of Athens, Panepistimiopolis, Athens 157-84, Greece
A. MELAS
Affiliation:
Department of Mathematics, University of Athens, Panepistimiopolis, Athens 157-84, Greece
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Abstract

We examine the range of universal Taylor series. We prove that every universal Taylor series on the unit disc assumes every complex number, with one possible exception, infinitely often. On the other hand, we prove that on any simply connected domain there exist universal functions that omit one value.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 4 , July 2000 , pp. 458 - 464
Copyright
© The London Mathematical Society 2000

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