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On the Coefficients and the Growth of Gap Power Series

Gaier, Dieter (1966) On the Coefficients and the Growth of Gap Power Series. SIAM Journal on Numerical Analysis, 3 (2). pp. 248-265. ISSN 0036-1429. doi:10.1137/0703019.

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In this paper we are interested in the limiting case, in which not the behavior of f in an angle, but only on a radius, for example z = x > 0, is known. Fabry gaps no longer suffice to get information about the growth of m(r) = [...], since already Pólya pointed out [11, p. 636] that there exist entire functions with Fabry gaps (even [...]), which are bounded for x > 0.

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Additional Information:©1966 Society for Industrial and Applied Mathematics. Received by the editors April 2, 1965. Dedicated to Professor J.L. Walsh on the occasion of his seventieth birthday. Mathematisches Institut der Universität, Giessen, Germany, and California Institute of Technology, Pasadena, California. This research was supported in part by the Office of Naval Research.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
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Deposited On:22 Apr 2008
Last Modified:08 Nov 2021 21:06

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