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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



An inequality for the eigenvalues of a class of self-adjoint operators

Author: William Stenger
Journal: Bull. Amer. Math. Soc. 73 (1967), 487-490
MathSciNet review: 0208385
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  • 1. Alexander Weinstein, The intermediate problems and the maximum-minimum theory of eigenvalues, J. Math. Mech. 12 (1963), 235–245. MR 0155083
  • 2. Alexander Weinstein, An invariant fomulation of the new maximum-minimum theory of eigenvalues, J. Math. Mech. 16 (1966), 213–218. MR 0212604
  • 3. W. Stenger, On Poincaré's bounds for higher eigenvalues, Bull. Amer. Math. Soc. 72 (1966), 715-718.
  • 4. W. Stenger, The maximum-minimum principle for the eigenvalues of unbounded operators, Notices Amer. Math. Soc. 13 (1966), 731.
  • 5. N. Aronszajn, Rayleigh-Ritz and A. Weinstein methods for approximation of eigenvalues. I. Operators in a Hilbert space, Proc. Nat. Acad. Sci. U. S. A. 34 (1948), 474–480. MR 0027955
  • 6. H. L. Hamburger and M. E. Grimshaw, Linear Transformations in 𝑛-Dimensional Vector Space. An Introduction to the Theory of Hilbert Space, Cambridge, at the University Press, 1951. MR 0041355
  • 7. Gaetano Fichera, Linear elliptic differential systems and eigenvalue problems, Lecture Notes in Mathematics, vol. 8, Springer-Verlag, Berlin-New York, 1965. MR 0209639
  • 8. S. H. Gould, Variational methods for eigenvalue problems. An introduction to the Weinstein method of intermediate problems, Second edition, revised and enlarged. Mathematical Expositions, No. 10, University of Toronto Press, Toronto, Ont.; Oxford University Press, London, 1966. MR 0209662
  • 9. J. B. Diaz, Upper and lower bounds for eigenvalues, Inst. for Fluid Dynamics and Appl, Math., Univ. of Maryland, College Park, Md., 1956. MR 0093907
  • 10. H. Weyl, Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen, Math. Ann. 71 (1911), 441-469.

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