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ON POLYNOMIAL SEQUENCES WITH RESTRICTED GROWTH NEAR INFINITY

Published online by Cambridge University Press:  15 March 2002

J. MÜLLER  and
A. YAVRIAN
J. MÜLLER
Affiliation:
University of Trier, FB IV, Mathematics, D-54286 Trier, Germanyjmueller@uni-trier.de
A. YAVRIAN
Affiliation:
Yerevan State University, Dept. of Mathematics, Alex Manoogian Str. 1, 375049 Yerevan, Armeniaayavrian@ysu.am
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Abstract

Let (Pn) be a sequence of polynomials which converges with a geometric rate on some arc in the complex plane to an analytic function. It is shown that if the sequence has restricted growth on a closed plane set E which is non-thin at ∞, then the limit function has a maximal domain of existence, and (Pn) converges with a locally geometric rate on this domain. If (snk) is a sequence of partial sums of a power series, a similar growth restriction on E forces the power series to have Ostrowski gaps. Moreover, the requirement of non-thinness of E at ∞ is necessary for these conclusions.

Type
PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 2 , March 2002 , pp. 189 - 199
Copyright
© 2002 The London Mathematical Society

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