Construction of Reproducing Kernel Hilbert Spaces Associated with the Laplace--Bessel Operator

Elina Shishkina

Construction of Reproducing Kernel Hilbert Spaces Associated with the Laplace--Bessel Operator

Functional Analysis 2026-07-13 v1

Authors: Elina Shishkina

Abstract

Motivated by applications to the study of problems for partial differential equations with Bessel operator, we introduce a new reproducing kernel Hilbert spaces (RKHS) which is fractional weighted Sobolev space with positive definite kernel. As an application, we obtain a simple and practical approximate solution to the singular Poisson equation.

Keywords

reproducing kernel Hilbert space Laplace-Bessel operator fractional weighted Sobolev space positive definite kernel singular Poisson equation

Cite

@article{arxiv.2607.11155,
  title  = {Construction of Reproducing Kernel Hilbert Spaces Associated with the Laplace--Bessel Operator},
  author = {Elina Shishkina},
  journal= {arXiv preprint arXiv:2607.11155},
  year   = {2026}
}