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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. http://resolver.caltech.edu/CaltechAUTHORS:GAIsiamjna66

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Abstract

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.


Item Type:Article
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.
Record Number:CaltechAUTHORS:GAIsiamjna66
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:GAIsiamjna66
Alternative URL:http://dx.doi.org/10.1137/0703019
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10283
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:22 Apr 2008
Last Modified:26 Dec 2012 09:58

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