Absolute continuity of periodic Schrödinger operators with potentials in the Kato class

Zhongwei Shen

doi:10.1215/ijm/1258138157

Absolute continuity of periodic Schrödinger operators with potentials in the Kato class

Zhongwei Shen

Mathematics

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

5 Scopus citations

Abstract

We consider the Schrödinger operator - Δ + V in ℝ^d with periodic potential V in the Kato class. We show that, if d = 2 or d = 3, the spectrum of - Δ + V is purely absolutely continuous.

Original language	English
Pages (from-to)	873-893
Number of pages	21
Journal	Illinois Journal of Mathematics
Volume	45
Issue number	3
DOIs	https://doi.org/10.1215/ijm/1258138157
State	Published - 2001

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Mathematics (all)

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title = "Absolute continuity of periodic Schr{\"o}dinger operators with potentials in the Kato class",

abstract = "We consider the Schr{\"o}dinger operator - Δ + V in ℝd with periodic potential V in the Kato class. We show that, if d = 2 or d = 3, the spectrum of - Δ + V is purely absolutely continuous.",

author = "Zhongwei Shen",

year = "2001",

doi = "10.1215/ijm/1258138157",

language = "English",

volume = "45",

pages = "873--893",

number = "3",

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T1 - Absolute continuity of periodic Schrödinger operators with potentials in the Kato class

AU - Shen, Zhongwei

PY - 2001

Y1 - 2001

N2 - We consider the Schrödinger operator - Δ + V in ℝd with periodic potential V in the Kato class. We show that, if d = 2 or d = 3, the spectrum of - Δ + V is purely absolutely continuous.

AB - We consider the Schrödinger operator - Δ + V in ℝd with periodic potential V in the Kato class. We show that, if d = 2 or d = 3, the spectrum of - Δ + V is purely absolutely continuous.

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U2 - 10.1215/ijm/1258138157

DO - 10.1215/ijm/1258138157

M3 - Article

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SN - 0019-2082

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EP - 893

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

IS - 3

ER -

Absolute continuity of periodic Schrödinger operators with potentials in the Kato class

Abstract

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