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Bulletin of the American Mathematical Society
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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References | Additional Information

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

  • 1. Alexander Weinstein, The intermediate problems and the maximum-minimum theory of eigenvalues, J. Math. Mech. 12 (1963), 235–245. MR 0155083 (27 #5025)
  • 2. Alexander Weinstein, An invariant fomulation of the new maximum-minimum theory of eigenvalues, J. Math. Mech. 16 (1966), 213–218. MR 0212604 (35 #3475)
  • 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 (10,382a)
  • 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 (12,836b)
  • 7. Gaetano Fichera, Linear elliptic differential systems and eigenvalue problems, Lecture Notes in Mathematics, vol. 8, Springer-Verlag, Berlin-New York, 1965. MR 0209639 (35 #536)
  • 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 (35 #559)
  • 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 (20 #427)
  • 10. H. Weyl, Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen, Math. Ann. 71 (1911), 441-469.


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1967-11789-0
PII: S 0002-9904(1967)11789-0