On a nonlocal integral operator commuting with the Laplacian and the Sturm–Liouville problem: Low rank perturbations of the operator

Author:

Hermi Lotfi1ORCID,Saito Naoki2ORCID

Affiliation:

1. Department of Mathematics and Statistics, Florida International University 1 , Miami, Florida 33199, USA

2. Department of Mathematics, University of California 2 , One Shields Avenue, Davis, California 95616, USA

Abstract

We reformulate all general real coupled self-adjoint boundary value problems as integral operators and show that they are all finite rank perturbations of the free space Green’s function on the real line. This free space Green’s function corresponds to the nonlocal boundary value problem proposed earlier by Saito [Appl. Comput. Harmon. Anal. 25, 68–97 (2008)]. We prove these perturbations to be polynomials of rank up to 4. They encapsulate in a fundamental way the corresponding boundary conditions.

Funder

National Science Foundation

Office of Naval Research

California Community Foundation

Publisher

AIP Publishing

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