A New Proof of the Sharp Gordon's Lemma: No Eigenvalues for Schr\"odinger Operators with Almost Repetition Potentials

TL;DR

This paper offers a new proof of Gordon's lemma, confirming the absence of eigenvalues in Schr"odinger operators with almost repetition potentials, extending previous results by Jitomirskaya-Simon and Jitomirskaya-Liu.

Contribution

It provides a novel proof of the sharp Gordon's lemma, strengthening the theoretical understanding of spectral properties of Schr"odinger operators with almost repetitive potentials.

Findings

Confirmed absence of eigenvalues for specified Schr"odinger operators

Extended previous results with a new proof technique

Strengthened theoretical foundation for spectral analysis

Abstract

Building on the work of Jitomirskaya-Simon and Jitomirskaya-Liu, who established the absence of eigenvalues for Schr\"odinger operators with almost reflective repetition potentials, we provide a new proof of the sharp Gordon's lemma, which asserts the absence of eigenvalues for Schr\"odinger operators with almost repetition potentials.