Some properties of the resolvent kernels for continuous bi-Carleman kernels

TL;DR

This paper demonstrates that resolvent kernels for certain continuous bi-Carleman kernels can be uniformly approximated by resolvent kernels of Hilbert-Schmidt subkernels at regular values within a strong convergence region.

Contribution

It establishes a new approximation method for resolvent kernels of bi-Carleman kernels using Hilbert-Schmidt subkernels, expanding understanding of their properties.

Findings

Resolvent kernels can be expressed as uniform limits of Hilbert-Schmidt resolvent kernels.

The results apply at regular values within a strong convergence region.

The approach enhances the analysis of bi-Carleman kernels in integral equations.

Abstract

We prove that, at regular values lying in a strong convergence region, the resolvent kernels for a continuous bi-Carleman kernel vanishing at infinity can be expressed as uniform limits of sequences of resolvent kernels for its approximating subkernels of Hilbert-Schmidt type