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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] Evans M. Harrell II, Singular perturbation potentials, Ann. Physics 105 (1977), no. 2, 379–406. MR 0449317, https://doi.org/10.1016/0003-4916(77)90246-9
  • [3] Tosio Kato, On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan 4 (1949), 334–339. MR 0038738, https://doi.org/10.1143/JPSJ.4.334
  • [4] Tosio Kato, On the convergence of the perturbation method. I, Progress Theoret. Physics 4 (1949), 514–523. MR 0034510
  • [5] Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473
  • [6] Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York-London, 1972. MR 0493419
    Michael Reed and Barry Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0493420
    Michael Reed and Barry Simon, Methods of modern mathematical physics. IV. Analysis of operators, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 0493421
  • [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