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A New Proof of the Sharp Gordon's Lemma: No Eigenvalues for Schrödinger Operators with Almost Repetition Potentials

Wencai Liu

Abstract

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

A New Proof of the Sharp Gordon's Lemma: No Eigenvalues for Schrödinger Operators with Almost Repetition Potentials

Abstract

Building on the work of Jitomirskaya-Simon and Jitomirskaya-Liu, who established the absence of eigenvalues for Schrödinger operators with almost reflective repetition potentials, we provide a new proof of the sharp Gordon's lemma, which asserts the absence of eigenvalues for Schrödinger operators with almost repetition potentials.
Paper Structure (2 sections, 4 theorems, 29 equations)

This paper contains 2 sections, 4 theorems, 29 equations.

Table of Contents

  1. Introduction
  2. Proof of Theorem \ref{['mthm']}

Key Result

Theorem 1.1

Assume $\gamma > \mathcal{L}(E)$. Then the eigen-equation $Hu = Eu$ has no $\ell^2(\mathbb{Z})$ solutions.

Theorems & Definitions (7)

  • Theorem 1.1
  • Corollary 1.2
  • Corollary 1.3
  • Remark 1
  • Lemma 2.1
  • proof
  • proof : Proof of Theorem \ref{['mthm']}