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Weak Bloch property for discrete magnetic Schrödinger operators

Published online by Cambridge University Press:  22 January 2016

Yusuke Higuchi  and
Tomoyuki Shirai
Yusuke Higuchi
Affiliation:
Mathematics Laboratories, College of Arts and Sciences, Showa University, 4562 Kamiyoshida, Fujiyoshida, Yamanashi, 403-0005, Japan, higuchi@cas.showa-u.ac.jp
Tomoyuki Shirai
Affiliation:
Mathematics Laboratories, College of Arts and Sciences, Showa University, 4562 Kamiyoshida, Fujiyoshida, Yamanashi, 403-0005, Japan, higuchi@cas.showa-u.ac.jp
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Abstract

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For a magnetic Schröodinger operator on a graph, which is a generalization of classical Harper operator, we study some spectral properties: the Bloch property and the behaviour of the bottom of the spectrum with respect to magnetic fields. We also show some examples which have interesting properties.

Keywords

Primary 58G25Secondary 05C50
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 161 , March 2001 , pp. 127 - 154
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

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