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An Exposition of the Connection between Limit-Periodic Potentials and Profinite Groups

Published online by Cambridge University Press:  12 May 2010

Z. Gan
Z. Gan*
Affiliation:
Department of Mathematics, Rice University, 77005 Houston, USA
*
* E-mail: zheng.gan@rice.edu
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Abstract

We classify the hulls of different limit-periodic potentials and show that the hull of a limit-periodic potential is a procyclic group. We describe how limit-periodic potentials can be generated from a procyclic group and answer arising questions. As an expository paper, we discuss the connection between limit-periodic potentials and profinite groups as completely as possible and review some recent results on Schrödinger operators obtained in this context.

Keywords

profinite grouplimit-periodic potentialSchrödinger operator
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 4: Spectral problems. Issue dedicated to the memory of M. Birman , 2010 , pp. 158 - 174
Copyright
© EDP Sciences, 2010

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Footnotes

Dedicated to the memory of M. S. Birman

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