Illinois Journal of Mathematics

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

Zhongwei Shen

Full-text: Open access

Abstract

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

Article information

Source
Illinois J. Math., Volume 45, Number 3 (2001), 873-893.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138157

Digital Object Identifier
doi:10.1215/ijm/1258138157

Mathematical Reviews number (MathSciNet)
MR1879241

Zentralblatt MATH identifier
1001.35029

Subjects
Primary: 35J10: Schrödinger operator [See also 35Pxx]
Secondary: 47A10: Spectrum, resolvent 47F05: Partial differential operators [See also 35Pxx, 58Jxx] (should also be assigned at least one other classification number in section 47) 81Q10: Selfadjoint operator theory in quantum theory, including spectral analysis

Citation

Shen, Zhongwei. Absolute continuity of periodic Schrödinger operators with potentials in the Kato class. Illinois J. Math. 45 (2001), no. 3, 873--893. doi:10.1215/ijm/1258138157. https://projecteuclid.org/euclid.ijm/1258138157


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