Lower bounds for the counting function of integral operators

TL;DR

This paper establishes a lower bound on the number of negative eigenvalues of certain integral operators with continuous kernels, using integral estimates of the kernel.

Contribution

It provides a new lower bound estimate for negative eigenvalues of integral operators based on kernel integrals, advancing spectral theory understanding.

Findings

Lower bound for negative eigenvalues derived

Estimate depends on integrals of the kernel

Applicable to operators with continuous kernels

Abstract

The paper presents a lower bound for the number of negative eigenvalues of an integral operator with continuous kernel K lying below a nonpositive number t. The estimate is given in terms of some integrals of K.