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On the measure of the spectrum for the almost Mathieu operator

Avron, J. and v. Mouche, P. H. M. and Simon, B. (1990) On the measure of the spectrum for the almost Mathieu operator. Communications in Mathematical Physics, 132 (1). pp. 103-118. ISSN 0010-3616. https://resolver.caltech.edu/CaltechAUTHORS:20171107-100226114

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Abstract

We obtain partial results on the conjecture that for the almost Mathieu operator at irrational frequency, α, the measure of the spectrum, S(α, λ, ϑ)=|4–2|λ‖. For |λ|≠2 we show that if α_n is rational and α_n→α irrational, then S+(α_n,λ,θ)→|4−2|λ||.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/BF02278001DOIArticle
https://link.springer.com/article/10.1007%2FBF02278001PublisherArticle
http://rdcu.be/ybLDPublisherFree ReadCube access
ORCID:
AuthorORCID
Simon, B.0000-0003-2561-8539
Additional Information:© 1990 Springer-Verlag. Received: 04 December 1989. Research partially supported by U.S. NSF grant number DMS-8801918 and by BSF under grant number 88-00325.
Funders:
Funding AgencyGrant Number
NSFDMS-8801918
Binational Science Foundation (USA-Israel)88-00325
Issue or Number:1
Record Number:CaltechAUTHORS:20171107-100226114
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171107-100226114
Official Citation:Avron, J., v. Mouche, P.H.M. & Simon, B. Commun.Math. Phys. (1990) 132: 103. https://doi.org/10.1007/BF02278001
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83025
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Nov 2017 18:17
Last Modified:03 Oct 2019 19:01

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