Abstract and Applied Analysis

Best Polynomial Approximation in L p -Norm and (p,q) -Growth of Entire Functions

Mohamed El Kadiri and Mohammed Harfaoui

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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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Abstr. Appl. Anal., Volume 2013 (2013), Article ID 845146, 9 pages.

First available in Project Euclid: 18 April 2013

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El Kadiri, Mohamed; Harfaoui, Mohammed. Best Polynomial Approximation in ${L}^{p}$ -Norm and $\mathrm{\left(p,q\right)}$ -Growth of Entire Functions. Abstr. Appl. Anal. 2013 (2013), Article ID 845146, 9 pages. doi:10.1155/2013/845146. https://projecteuclid.org/euclid.aaa/1366306771

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