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2013 Best Polynomial Approximation in L p -Norm and (p,q) -Growth of Entire Functions
Mohamed El Kadiri, Mohammed Harfaoui
Abstr. Appl. Anal. 2013: 1-9 (2013). DOI: 10.1155/2013/845146


The classical growth has been characterized in terms of approximation errors for a continuous function on [ - 1,1 ] by Reddy (1970), and a compact K 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 ( ( p , q ) -growth) of entire functions in n by means of the best polynomial approximation in terms of L p -norm, with respect to the set Ω r = { z C n ; exp V K ( z ) r } , where V K = sup { (1/ d) log | P d | , P d polynomial of degree d , P d K 1 } is the Siciak's extremal function on an L -regular nonpluripolar compact K is not pluripolar.


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Mohamed El Kadiri. Mohammed Harfaoui. "Best Polynomial Approximation in L p -Norm and (p,q) -Growth of Entire Functions." Abstr. Appl. Anal. 2013 1 - 9, 2013.


Published: 2013
First available in Project Euclid: 18 April 2013

zbMATH: 1264.32002
MathSciNet: MR3035199
Digital Object Identifier: 10.1155/2013/845146

Rights: Copyright © 2013 Hindawi

Vol.2013 • 2013
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