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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. doi:10.1007/BF02278001.

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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||.

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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.
Funding AgencyGrant Number
Binational Science Foundation (USA-Israel)88-00325
Issue or Number:1
Record Number:CaltechAUTHORS:20171107-100226114
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Official Citation:Avron, J., v. Mouche, P.H.M. & Simon, B. Commun.Math. Phys. (1990) 132: 103.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83025
Deposited By: Tony Diaz
Deposited On:07 Nov 2017 18:17
Last Modified:15 Nov 2021 19:54

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