Limit-Periodic Schr\"odinger Operators With Lipschitz Continuous IDS

TL;DR

This paper constructs limit-periodic Schrödinger operators with Lipschitz continuous integrated density of states, advancing understanding of spectral properties in inverse spectral theory.

Contribution

It demonstrates the existence of such operators using the inverse spectral theoretic KAM approach, which was not previously established.

Findings

Existence of limit-periodic Schrödinger operators with Lipschitz continuous IDS

Application of inverse spectral theoretic KAM method to construct these operators

Provides new insights into spectral regularity properties

Abstract

We show that there exist limit-periodic Schr\"odinger operators such that the associated integrated density of states is Lipschitz continuous. These operators arise in the inverse spectral theoretic KAM approach of P\"oschel.