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Random perturbations of singular spectra


Author: James S. Howland
Journal: Proc. Amer. Math. Soc. 112 (1991), 1009-1011
MSC: Primary 47A55; Secondary 47A10, 81Q10, 82B44
DOI: https://doi.org/10.1090/S0002-9939-1991-1037208-5
MathSciNet review: 1037208
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Abstract: The singular parts of the self-adjoint operators $ T$ and $ H = T + V$ are mutually singular for "almost every" bounded perturbation $ V$.


References [Enhancements On Off] (What's this?)

  • [1] W. F. Donoghue, On the perturbation of spectra, Comm. Pure Appl. Math. 18 (1965), 559-579. MR 0190761 (32:8171)
  • [2] J. S. Howland, Perturbation theory of dense point spectra, J. Funct. Anal. 74 (1987), 52-80. MR 901230 (89b:47023)
  • [3] T. Kato, Perturbation Theory for linear operators, Springer-Verlag, New York, 1966. MR 0203473 (34:3324)
  • [4] M. Reed and B. Simon, Methods of modern mathematical physics. II, Academic Press, New York, 1978. MR 751959 (85e:46002)
  • [5] B. Simon and T. Wolff, Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Comm. Pure Appl. Math. 39 (1986), 75-90. MR 820340 (87k:47032)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1037208-5
Article copyright: © Copyright 1991 American Mathematical Society

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