On absolute continuity of the spectrum of periodic Schrödinger operators

Ihyeok Seo

doi:10.1007/s00605-015-0815-7

On absolute continuity of the spectrum of periodic Schrödinger operators

Ihyeok Seo

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	893-912
Number of pages	20
Journal	Monatshefte fur Mathematik
Volume	180
Issue number	4
DOIs	https://doi.org/10.1007/s00605-015-0815-7
State	Published - 1 Aug 2016

Keywords

Absolute continuity
Schrödinger operators
Spectrum

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10.1007/s00605-015-0815-7

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abstract = "In this paper we find a new condition on a real periodic potential for which the self-adjoint Schr{\"o}dinger 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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AB - 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.

KW - Absolute continuity

KW - Schrödinger operators

KW - Spectrum

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On absolute continuity of the spectrum of periodic Schrödinger operators

Abstract

Keywords

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