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

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.