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A Remark on the Hull of a Multi-Dimensional Limit-Periodic Potential

Published online by Cambridge University Press:  28 January 2013

Z. Gan
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Abstract

We discuss the hull of a multi-dimensional limit-periodic potential and show that such a hull is an inverse limit of product cyclic groups. We present the result in an explicit way, which will be useful for a future study of multi-dimensional limit-periodic Schrödinger operators.

Keywords

limit-periodic potentialinverse limit
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 1: Harmonic analysis , 2013 , pp. 75 - 81
Copyright
© EDP Sciences, 2013

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References

Références

Avila, A., On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators, Commun. Math. Phys. 288 (2009), 907–918 CrossRefGoogle Scholar
Avron, J., Simon, B., Almost periodic Schrödinger operators. I. Limit periodic potentials, Commun. Math. Phys. 82 (1981), 101–120 CrossRefGoogle Scholar
Damanik, D., Gan, Z., Spectral properties of limit-periodic Schrödinger operators, Commun. Pure Appl. Anal. 10 (2011), 859–871 CrossRefGoogle Scholar
Damanik, D., Gan, Z., Limit-periodic Schrödinger operators in the regime of positive Lyapunov exponents, J. Funct. Anal. 258 (2010), 4010–4025 CrossRefGoogle Scholar
Damanik, D., Gan, Z., Limit-periodic Schröinger operators with uniformly localized eigenfunctions, J. d’Analyse Math, 115 (2011), 33–49 CrossRefGoogle Scholar
D. Damanik, Z. Gan, Limit-Periodic Schrödinger Operators on Zd : Uniform Localization, preprint
del Rio, R., Jitomirskaya, S., Last, Y., Simon, B., What is localization?, Phys. Rev. Lett. 75 (1995), 117–119 CrossRefGoogle Scholar
del Rio, R., Jitomirskaya, S., Last, Y., Simon, B., Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization, J. Anal. Math. 145 (1997), 312–322 Google Scholar
Gan, Z., An exposition of the connection between limit-periodic potentials and profinite groups, Math. Model. Nat. Phenom. 5:4 (2010), 158–174 CrossRefGoogle Scholar
J. Wilson. Profinite Groups, Oxford University Press, New York, USA, 1998