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Generalizations of Temple's inequality


Author: Evans M. Harrell
Journal: Proc. Amer. Math. Soc. 69 (1978), 271-276
MSC: Primary 49G20
DOI: https://doi.org/10.1090/S0002-9939-1978-0487733-4
MathSciNet review: 0487733
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Abstract: T. Kato's little-known generalization of a classic variational inequality for eigenvalues is extended to the case of normal operators and briefly discussed.


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

  • [1] W. M. Greenlee, Perturbation of bounded states of the radial equation by potentials with a repulsive hard core--first order asymptotics, J. Functional Analysis (to appear).
  • [2] E. Harrell, Singular perturbation potentials, Ann. Physics 105 (1977), 379-405. MR 0449317 (56:7622)
  • [3] T. Kato, On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan 4 (1949), 334-339. MR 0038738 (12:447b)
  • [4] -, On the convergence of the perturbation method. I, Progr. Theoret. Phys. 4 (1949), 514-523; II.1, Ibid. 5 (1950), 95-101; II.2, Ibid. 5 (1950), 207-212. MR 0034510 (11:599a)
  • [5] -, Perturbation theory for linear operators, Grundlehren Math. Wiss., Band 132, Springer-Verlag, New York, 1966. MR 0203473 (34:3324)
  • [6] M. Reed and B. Simon, Methods of modern mathematical physics. I: Functional analysis, Academic Press, New York, 1972. MR 0493419 (58:12429a)
  • [7] G. Temple, The theory of Rayleigh's principle as applied to continuous systems, Proc. Roy. Soc. London Ser. A 119 (1928), 276-293.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0487733-4
Keywords: Temple's inequality, bounds for eigenvalues, normal operators, unitary operators, trial functions
Article copyright: © Copyright 1978 American Mathematical Society

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