On absolute continuity of the spectrum of periodic Schrödinger operators

2014/06/13 by Seo, Ihyeok
#FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1406.3419

Abstract

In this paper we find a new condition on a real periodic potential for which the self-adjoint Schrödinger operator may be defined by a quadratic form and the spectrum of the operator is purely absolutely continuous. This is based on resolvent estimates and spectral projection estimates in weighted L² spaces on the torus, and an oscillatory integral theorem.

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