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On an infinite series of Abel occurring in the theory of interpolation

Luxemburg, W. A. J. (1975) On an infinite series of Abel occurring in the theory of interpolation. Journal of Approximation Theory, 13 (4). pp. 363-374. ISSN 0021-9045.

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The purpose of this paper is to show that for a certain class of functions f which are analytic in the complex plane possibly minus (−∞, −1], the Abel series ! is convergent for all β>0. Its sum is an entire function of exponential type and can be evaluated in terms of f. Furthermore, it is shown that the Abel series of f for small β>0 approximates f uniformly in half-planes of the form Re(z) ⩾ − 1 + δ, δ>0. At the end of the paper some special cases are discussed.

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Additional Information:© 1975 Published by Elsevier Inc. Under an Elsevier user license. Communicated by P. L. Butzer. Dedicated to Professor G. G. Lorentz on the occasion of his sixty-fifth birthday. Work on this paper was supported in part by NSF Grant 23392.
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Issue or Number:4
Record Number:CaltechAUTHORS:20181009-135412183
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Official Citation:W.A.J Luxemburg, On an infinite series of Abel occurring in the theory of interpolation, Journal of Approximation Theory, Volume 13, Issue 4, 1975, Pages 363-374, ISSN 0021-9045, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90201
Deposited By: Joy Painter
Deposited On:10 Oct 2018 20:16
Last Modified:03 Oct 2019 20:23

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