Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-19T16:49:41.007Z Has data issue: false hasContentIssue false

A Remark on the Hull of a Multi-Dimensional Limit-PeriodicPotential

Published online by Cambridge University Press:  28 January 2013

Get access

Abstract

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

Type
Research Article
Copyright
© EDP Sciences, 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

Avila, A., On the spectrum and Lyapunov exponent of limit periodic Schrödinger operators, Commun. Math. Phys. 288 (2009), 907918 CrossRefGoogle Scholar
Avron, J., Simon, B., Almost periodic Schrödinger operators. I. Limit periodic potentials, Commun. Math. Phys. 82 (1981), 101120 CrossRefGoogle Scholar
Damanik, D., Gan, Z., Spectral properties of limit-periodic Schrödinger operators, Commun. Pure Appl. Anal. 10 (2011), 859871 CrossRefGoogle Scholar
Damanik, D., Gan, Z., Limit-periodic Schrödinger operators in the regime of positive Lyapunov exponents, J. Funct. Anal. 258 (2010), 40104025 CrossRefGoogle Scholar
Damanik, D., Gan, Z., Limit-periodic Schröinger operators with uniformly localized eigenfunctions, J. d’Analyse Math, 115 (2011), 3349 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), 117119 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), 312322 Google Scholar
Gan, Z., An exposition of the connection between limit-periodic potentials and profinite groups, Math. Model. Nat. Phenom. 5:4 (2010), 158174 CrossRefGoogle Scholar
J. Wilson. Profinite Groups, Oxford University Press, New York, USA, 1998