A quantitative version of Gordon's Theorem for Jacobi and Sturm-Liouville operators

TL;DR

This paper presents a quantitative extension of Gordon's Theorem, providing conditions under which Jacobi matrices and Sturm-Liouville operators with complex coefficients have no eigenvalues, advancing spectral theory understanding.

Contribution

It introduces a quantitative version of Gordon's Theorem applicable to complex coefficient Jacobi and Sturm-Liouville operators, enhancing previous qualitative results.

Findings

Established absence of eigenvalues under new quantitative conditions

Extended Gordon's Theorem to complex coefficient operators

Provided analytical tools for spectral analysis of differential operators

Abstract

We prove a quantitative version of Gordon's Theorem concerning absence of eigenvalues for Jacobi matrices and Sturm-Liouville operators with complex coefficients.