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Analytic Continuation of Power Series by Regular Generalized Weighted Means

Published online by Cambridge University Press:  20 November 2018

Bruce L. R. Shawyer  and
Ludwig Tomm
Bruce L. R. Shawyer
Affiliation:
Department of MathematicsThe University of Western Ontario London, Ontario, CanadaN6A 5B7
Ludwig Tomm
Affiliation:
Universität UlmAbteilung für Mathematik IV Oberer Eselsberg D-7900 Ulm, West Germany
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Abstract

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The behaviour of summability transforms of power series outside their circles of convergence has been studied by many authors. In the case of the geometric series Luh [6] and Tomm [10] showed that there exist regular methods A which provide an analytic continuation into any given simply connected region G that contains the unit disc but not the point 1. Moreover, the Atransforms of the geometric series may be required to converge to any chosen analytic function on prescribed regions outside the unit circle. In this paper, these results are extended to power series representing other meromorphic functions. It is also shown that the summability methods involved may be chosen to be generalized weighted means previously introduced by Faulstich [1].

Keywords

40C0541A10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 4 , 01 December 1983 , pp. 454 - 463
Copyright
Copyright © Canadian Mathematical Society 1983

References

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