On the distribution of eigenvalues of non-selfadjoint operators

TL;DR

This paper establishes quantitative bounds on the eigenvalues of non-selfadjoint operators by leveraging the perturbation determinant and analyzing the zeros of associated holomorphic functions.

Contribution

It introduces a novel approach to bounding eigenvalues of non-selfadjoint operators using complex analysis techniques.

Findings

Derived explicit bounds for eigenvalues of non-selfadjoint operators

Reduced eigenvalue estimation to zeroes of holomorphic functions

Applicable to both bounded and unbounded operators

Abstract

We prove quantitative bounds on the eigenvalues of non-selfadjoint bounded and unbounded operators. We use the perturbation determinant to reduce the problem to one of studying the zeroes of a holomorphic function.