Eigenfunctions of a weighted Laplace operator in the whole space

被引：5

作者：

Arar, Nouria ^{[1
]}

Boulmezaoud, Tahar Z. ^{[2
]}

机构：

[1] Univ Mentouri, Dept Math, Constantine, Algeria

[2] Univ Versailles St Quentin En Yvelines, Lab Math Versailles, F-78035 Versailles, France

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 400卷 / 01期

关键词：

Laplace operator; Unbounded domains; Rational functions; Stereographic projection; Weighted spaces; HALF-SPACE;

D O I：

10.1016/j.jmaa.2012.06.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the spectrum of the weighted Laplacian rho(-1) Delta in the whole space R-n. We prove, under adequate conditions on rho(-1), that this spectrum is discrete and we derive an explicit formula for eigenvalues and eigenfunctions when rho(-1) = (vertical bar x vertical bar(2) + 1)(2). We get by the way a complete family of rational functions which are mutually orthogonal in a weighted L-2 space. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：161 / 173

页数：13

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