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:
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a)
its point spectrum is finite;
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b)
its singular continuous spectrum is empty;
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c)
its resolvent satisfies a class of a priori estimates.
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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)
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Communicated by B. Simon
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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
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DOI: https://doi.org/10.1007/BF01942331