On a nonlocal integral operator commuting with the Laplacian and the Sturm-Liouville problem: Low rank perturbations of the operator (with L. Hermi), Journal of Mathematical Physics, vol. 65, Article #043503, 2024.

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)]. These are polynomial perturbations of rank up to 4. They encapsulate in a fundamental way the corresponding boundary conditions.

Keywords: Integral operators; nonlocal boundary conditions; Green's functions; resolvent kernels; finite rank perturbations; general real coupled self-adjoint boundary conditions

  • Get the full paper (via arXiv:2211.07141 [math.SP]) : PDF file.
  • Get the official version via doi:10.1063/5.0187858.
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