Pacific Journal of Mathematics

Some isoperimetric inequalities for the eigenvalues of vibrating strings.

David C. Barnes

Article information

Source
Pacific J. Math., Volume 29, Number 1 (1969), 43-61.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102983142

Mathematical Reviews number (MathSciNet)
MR0244545

Zentralblatt MATH identifier
0194.27302

Subjects
Primary: 34.30
Secondary: 35.00

Citation

Barnes, David C. Some isoperimetric inequalities for the eigenvalues of vibrating strings. Pacific J. Math. 29 (1969), no. 1, 43--61. https://projecteuclid.org/euclid.pjm/1102983142


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References

  • [1] D. 0. Banks, Bounds or the eigenvalues of some vibrating systems. Pacific J. Math. (2) 10 (1960), 439-474.
  • [2] D. 0. Banks, Upper bounds for the eigenvalues of some vibrating systems, Pacific J. Math. (4) 11 (1961),1183-1203. 3# fAn integral inequality, Proc. Amer. Math. Soc. (5) 14 (1963),823-828.
  • [4] D. 0. Banks, Bounds for eigenvalues and generalized convexity, Pacific J. Math. (4) 12 (1963), 1031-1052.
  • [5] D. 0. Banks, Lower bounds for the eigenvalues of the vibrating string whose density satisfies a Lipschitz condition, Pacific J. Math. (1) 20 (1967), 393-410.
  • [6] A. M. Bruckner and E. Ostrow, Some function classes related to the class of convex function, Pacific J. Math. (4) 12 (1962), 1203-1215.
  • [7] R. Courant, and D. Hubert, Methods of mathematical physics, Interscience, New York, 1953.
  • [8] M. Krein, On certain problems on the maximum and minimumofcharacteristic values and on Lyapunov zones of stability, Amer. Math. Soc. Trans. (2) 1 (1955),163-187.
  • [9] E. Makai, ber die Nullstellen von Funktionen die Losungen Sturm-Liouville' scher Differentialgleichungensind, Comm. Math. Helv. 16 (1943), 153-199.
  • [10] Z. Nehari, Extremal problems for a class of functionalsdefined on convex sets, Bull. Amer. Math. Soc. 73 (1967),584-591.
  • [11] Z. Nehari, Oscillation criteria for second order linear differential equations, Trans. Amer. Math. Soc. 85 (1957),428-445.
  • [12] B. Schwarz, On the extrema of the frequencies of nonhomogeneous stringswith equimeasurable densities, J. Math. Mech. 1O (1961), 401-422.
  • [13] A. Smirnov, Tables of Airy functions,Pergamon Press.