Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898210 | Applied and Computational Harmonic Analysis | 2018 | 25 Pages |
Abstract
In this article we prove the existence, uniqueness, and simplicity of a negative eigenvalue for a class of integral operators whose kernel is of the form |xây|Ï, 0<Ïâ¤1, x,yâ[âa,a]. We also provide two different ways of producing recursive formulas for the Rayleigh functions (i.e., recursion formulas for power sums) of the eigenvalues of this integral operator when Ï=1, providing means of approximating this negative eigenvalue. These methods offer recursive procedures for dealing with the eigenvalues of a one-dimensional Laplacian with non-local boundary conditions which commutes with an integral operator having a harmonic kernel. The problem emerged in recent work by one of the authors [48]. We also discuss extensions in higher dimensions and links with distance matrices.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Lotfi Hermi, Naoki Saito,