Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010Spectral problems. Issue dedicated to the memory of M. Birman
|Page(s)||158 - 174|
|Published online||12 May 2010|
An Exposition of the Connection between Limit-Periodic Potentials and Profinite Groups
Department of Mathematics, Rice University, 77005
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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.
Mathematics Subject Classification: 47B36 / 22D12 / 81Q10
Key words: profinite group / limit-periodic potential / Schrödinger operator
© EDP Sciences, 2010
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