Abstract
We exhibit an example of a one-dimensional discrete Schrödinger operator with almost periodic potential for which the steps of the density of states do not belong to the frequency module. This example is suggested by theK-theory [3].
Similar content being viewed by others
References
Avron, J., Simon, B.: Almost periodic Schrödinger operators. II. The density of sates and the Aubry Andre model (in preparation)
Bellissard, J., Testard, D.: Almost periodic hamiltonian: an algebraic approach. Marseille Preprint (1981)
Bellissard, J., Lima, R., Testard, D.: Almost random operators:K-theory and spectral properties (in preparation)
Connes, A.: Adv. Math.39, 31 (1981)
Khintchine, A.: Continued fractions. Transl. by P. Wynn. Groningen: Nordhoff 1963
Moser, J.: An example of Schrödinger equation with almost periodic potential and nowhere dense spectrum. ETH Preprint (1980)
Pimsner, M., Voiculescu, D.: J. Oper. Theor.4, 201–210 (1980)
Rieffel, M.A.: Irrational rotationC*-algebras. Short communication at the International Congress of Mathematicians 1978
Shubin, M.A.: Russ. Math. Surv.33 (2), 1 (1978), and references therein
One of us (J.B.) is indebted to S. Aubry for giving him this information
Weyl, H.: Über die Gleichverteilung von Zahlen nach Eins. Math. Ann.77, 313–352 (1916)
Pedersen, G.K.:C*-algebras and their automorphism groups. London, New York: Academic Press 1979
Author information
Authors and Affiliations
Additional information
Communicated by A. Jaffe
Rights and permissions
About this article
Cite this article
Bellissard, J., Scoppola, E. The density of states for almost periodic Schrödinger operators and the frequency module: A counter-example. Commun.Math. Phys. 85, 301–308 (1982). https://doi.org/10.1007/BF01254461
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01254461