Universal series induced by approximate identities and some relevant applications

JOURNAL OF APPROXIMATION THEORY

卷:163

Article

Nestoridis, Vassili²  Schmutzhard, Sebastian¹  Stefanopoulos, Vangelis³ 

[1] Univ Vienna, Fac Math, A-1090 Vienna, Austria

[2] Univ Athens, Dept Math, Panepistimiopolis 15784, Greece

[3] Univ Aegean, Dept Math, Karlovassi 83200, Samos, Greece

关键词: Universal series;    Wiener algebra;    Approximation to the identity;    Gauss kernel;    Poisson kernel;    Normal distribution;    Heat equation;    Laplace's equation;   

DOI  :  10.1016/j.jat.2011.06.001

来源: Elsevier

【 摘 要 】

We prove the existence of series Sigma a(n psi n) whose coefficients (a(n)) are in boolean AND(p>I) l(p) and whose terms (psi(n)) are translates by rational vectors in R-d of a family of approximations to the identity, having the property that the partial sums are dense in various spaces of functions such as Wiener's algebra W (C-0, l(l)), C-b(R-d), C-0(R-d), L-p(R-d), for every p is an element of [1, infinity), and the space of measurable functions. Applying this theory to particular situations, we establish approximations by such series to solutions of the heat and Laplace equations as well as to probability density functions. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free