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A forbidden set for embedded eigenvalues

Author: Rafael René del Río Castillo
Journal: Proc. Amer. Math. Soc. 121 (1994), 77-82
MSC: Primary 34L99; Secondary 34B20, 34B24, 47E05
MathSciNet review: 1191867
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Abstract: We study the problem of embedding eigenvalues to the spectrum of a Sturm-Liouville operator in the half axis when this spectrum is a perfect set. We prove the existence of an uncountable dense subset of the spectrum for which, by modifying the condition at the left or by locally perturbing the potential, it is not possible to add any eigenvalues.

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

  • [1] N. Aronszajn, On a problem of Weyl in the theory of singular Sturm-Liouville equations, Amer. J. Math. 79 (1957), 597-610. MR 0088623 (19:550b)
  • [2] R. R. del Rio Castillo, Embedded eigenvalues of Sturm-Liouville operators, Comm. Math. Phys. 142 (1991), 421-431. MR 1137069 (92h:47067)
  • [3] W. F. Donoghue, On the perturbation of spectra, Comm. Pure Appl. Math. 18 (1965), 559-579. MR 0190761 (32:8171)
  • [4] M. S. P. Eastham and H. Kalf, Schrödinger type operators with continuous spectra, Pitman Research Notes in Math., vol. 65, Longman Sci. Tech., Harlow, 1982. MR 667015 (84i:35107)
  • [5] N. K. Kundu, On some properties of symmetric derivatives, Ann. Polon. Math. 30 (1974), 9-18. MR 0346102 (49:10828)
  • [6] J. Weidmann, Spectral theory of ordinary differential operators, Lecture Notes in Math., vol. 1258, Springer-Verlag, New York, 1987. MR 923320 (89b:47070)

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Article copyright: © Copyright 1994 American Mathematical Society

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