Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Random quadratic forms

Authors: John Gregory and H. R. Hughes
Journal: Trans. Amer. Math. Soc. 347 (1995), 709-717
MSC: Primary 47B80; Secondary 34B24, 34C10, 34F05
MathSciNet review: 1254841
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The results of Boyce for random Sturm-Liouville problems are generalized to random quadratic forms. Order relationships are proved between the means of eigenvalues of a random quadratic form and the eigenvalues of an associated mean quadratic form. Finite-dimensional and infinite-dimensional examples that show these are the best possible results are given. Also included are some results for a general approximation theory for random quadratic forms.

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

  • [1] W. E. Boyce, Random eigenvalue problems, Probabilistic Methods in Applied Mathematics (A. T. Bharucha-Reid, ed.), Academic Press, New York, 1968, pp. 1-73. MR 0263171 (41:7776)
  • [2] -, On a conjecture concerning the means of the eigenvalues of random Sturm-Liouville boundary value problems, Quart. Appl. Math. 38 (1980), 241-245. MR 580882 (81i:34016)
  • [3] R. Courant and D. Hilbert, Methods of mathematical physics, vol. 1, Interscience, New York, 1953. MR 0065391 (16:426a)
  • [4] J. Gregory, An approximation theory for elliptic quadratic forms on Hilbert spaces: application to the eigenvalue problem for compact quadratic forms, Pacific J. Math. 37 (1970), 383-395. MR 0303311 (46:2449)
  • [5] -, Quadratic form theory and differential equations, Math. Sci. Engr., vol. 152, Academic Press, San Diego, CA, 1980. MR 599362 (82d:49001)
  • [6] M. R. Hestenes, Applications of the theory of quadratic forms in Hilbert space in the calculus of variations, Pacific J. Math. 1 (1951), 525-582. MR 0046590 (13:759a)
  • [7] K. Kreith, Lower estimates for zeros of stochastic Sturm-Liouville problems, Proc. Amer. Math. Soc. 92 (1984), 515-518. MR 760936 (86c:34115)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 47B80, 34B24, 34C10, 34F05

Retrieve articles in all journals with MSC: 47B80, 34B24, 34C10, 34F05

Additional Information

Keywords: Sturm-Liouville problem, random eigenvalues, continuity of eigenvalues
Article copyright: © Copyright 1995 American Mathematical Society

American Mathematical Society