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Limit points of partial sums of Taylor series

Part of: Series expansions

Published online by Cambridge University Press:  26 February 2010

V. Nestoridis
V. Nestoridis
Affiliation:
Department of Mathematics, University of Crete, P. O. Box 1470 Iraklion Crete, Greece.
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Extract

Fifty years ago Marcinkiewicz and Zygmund studied the circular structure of the limit points of the partial sums for (C, 1) summable Taylor series. More specifically, let

be a power series with complex coefficients, let

be the partial sums, and let

be the Cesàro averages. When the sequence σn(z) converges to a finite limit σ(Z), we say that the Taylor series is (C, 1) summable and σ(z) is the (C, 1) sum of the series. Concerning (C, 1) summable Taylor series Marcinkiewicz and Zygmund ([5], [6] Vol. II, p. 178) established the following theorem.

MSC classification

Secondary: 30B30: Boundary behavior of power series, over-convergence
Type
Research Article
Information
Mathematika , Volume 38 , Issue 2 , December 1991 , pp. 239 - 249
Copyright
Copyright © University College London 1991

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References

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