Abstract
We give a sufficient condition for a self-adjoint operator to have the following properties in a neighborhood of a pointE of its spectrum:
-
a)
its point spectrum is finite;
-
b)
its singular continuous spectrum is empty;
-
c)
its resolvent satisfies a class of a priori estimates.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Kato, T.: Perturbation theory for linear operators. Berlin, Heidelberg, New York: Springer 1966
Agmon, S.: Ann. Scuola Norm. Sup. Pisa, Ser. 4,2, 151–218 (1975)
Aguilar, J., Combes, J.M.: Commun. Math. Phys.22, 269–279 (1971)
Balslev, E., Combres, J.M.: Commun. Math. Phys.22, 280–294 (1971)
Reed, M., Simon, B.: Methods of modern mathematical physics. Tomes II and III. New York: Academic Press 1979
Enss, V.: Commun. Math. Phys.61, 285 (1978)
Simon, B.: Duke Math. J.46, 119–168 (1979)
Author information
Authors and Affiliations
Additional information
Communicated by B. Simon
Rights and permissions
About this article
Cite this article
Mourre, E. Absence of singular continuous spectrum for certain self-adjoint operators. Commun.Math. Phys. 78, 391–408 (1981). https://doi.org/10.1007/BF01942331
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01942331