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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 845146, 9 pages
http://dx.doi.org/10.1155/2013/845146
Research Article

Best Polynomial Approximation in -Norm and -Growth of Entire Functions

1Department of Mathematics, University Mohammed V-Agdal, 4 Avenue Ibn Battouta, BP 1014 RP, Rabat, Morocco
2Laboratory of Mathematics, Cryptography and Mechanical, F.S.T., University Hassan II Mohammedia, BP 146, 20650 Mohammedia, Morocco

Received 7 March 2012; Revised 16 December 2012; Accepted 16 December 2012

Academic Editor: Natig M. Atakishiyev

Copyright © 2013 Mohamed El Kadiri and Mohammed Harfaoui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The classical growth has been characterized in terms of approximation errors for a continuous function on by Reddy (1970), and a compact of positive capacity by Nguyen (1982) and Winiarski (1970) with respect to the maximum norm. The aim of this paper is to give the general growth ( -growth) of entire functions in by means of the best polynomial approximation in terms of -norm, with respect to the set , where is the Siciak's extremal function on an -regular nonpluripolar compact is not pluripolar.