Spectrum of partial integral operators with degenerate kernel

TL;DR

This paper analyzes the spectral properties of self-adjoint Fredholm-type partial integral operators with degenerate kernels on a specific function space, describing their essential and discrete spectra.

Contribution

It provides a detailed description of the essential and discrete spectra of such operators with degenerate kernels, advancing spectral theory understanding.

Findings

Characterization of the essential spectrum.

Description of the discrete spectrum.

Application to operators with degenerate kernels.

Abstract

In the paper we consider self-adjoint partial integral operators of Fredholm type $T$ with a degenerate kernel on the space $L_2([a,b]\times[c,d]).$ Essential and discrete spectra of $T$ are described.