International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 360180, 15 pages
doi:10.1155/2010/360180
Research Article

Generalized Order and Best Approximation of Entire Function in 𝐿 𝑝 -Norm

Mohammed Harfaoui

University Hassan II-Mohammedia, U.F.R Mathematics and Applications, F.S.T, BP 146, Mohammedia, Morocco

Received 7 March 2010; Accepted 26 December 2010

Academic Editor: Rodica Costin

Copyright © 2010 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 aim of this paper is the characterization of the generalized growth of entire functions of several complex variables by means of the best polynomial approximation and interpolation on a compact 𝐾 with respect to the set Ω 𝑟 = { 𝑧 ∈ 𝐂 𝑛 ; e x p 𝑉 𝐾 ( 𝑧 ) ≤ 𝑟 } , where 𝑉 𝐾 = s u p { ( 1 / 𝑑 ) l n | 𝑃 𝑑 | , 𝑃 𝑑 p o l y n o m i a l o f d e g r e e ≤ 𝑑 , ‖ 𝑃 𝑑 ‖ 𝐾 ≤ 1 } is the Siciak extremal function of a 𝐿 -regular compact 𝐾 .