Pacific Journal of Mathematics
- Pacific J. Math.
- Volume 4, Number 3 (1954), 467-480.
Asymptotic lower bounds for the frequencies of certain polygonal membranes.
Full-text: Open access
Article information
Source
Pacific J. Math. Volume 4, Number 3 (1954), 467-480.
Dates
First available in Project Euclid: 14 December 2004
Permanent link to this document
https://projecteuclid.org/euclid.pjm/1103044799
Mathematical Reviews number (MathSciNet)
MR0063784
Zentralblatt MATH identifier
0055.35507
Subjects
Primary: 65.0X
Citation
Forsythe, George E. Asymptotic lower bounds for the frequencies of certain polygonal membranes. Pacific J. Math. 4 (1954), no. 3, 467--480. https://projecteuclid.org/euclid.pjm/1103044799.
References
- [1] N. Aronszajn and A. Zeichner, A new type of auxiliary problem for approximation of eigenvalues by Weinstein's method, Technical Report 5, Oklahoma A. and M. College, Department of Mathematics, 1951.
- [2] DorothyL. Bernstein, Existencetheorems in partial differentialequations, Annals of Mathematics Studies, No. 23, Princeton University Press, 1950.
- [3] Lothar Collatz, Eigenwertaufgaben mit technischen Anwendungen, Akademische Verlagsges., Leipzig, 1949.
- [4] Chandler Davis,Estimating eigenvalues,Proc. Amer. Math. Soc. 3 (1952), 942-947.
- [5] George E. Forsythe, Asymptotic lower bounds for the fundamental frequency of convex membranes, multilithed typescript, National Bureau of Standards, Los Angeles, November 1953, 21 pp. (To appear in the Pacific Journal of Mathematics.)
- [6] L. V. Kantorovic and V.I. Krylov, Priblizennyemetody vyssegoanaliza (Ap- proximate methods of higher analysis ), 3rd edit., Moscow-Leningrad, 1950.Mathematical Reviews (MathSciNet): MR13:77b
- [7] Wilfred Kaplan, Advanced calculus, Addison-Wesley, Cambridge, 1952.
- [8] Tosio Kato, On the upper and lower bounds of eigenvalues, J. Phys. Soc. Japan 4(1949), 334-339.Mathematical Reviews (MathSciNet): MR12:447b
- [9] William Edmund Milne, Numerical solution of differential equations, Wiley, New York and Chapman-Hall, London, 1953.Mathematical Reviews (MathSciNet): MR16:864c
- [10] Zeev Nehari, Conformal mapping, McGraw-Hill, New York, Toronto, and London, 1952.Mathematical Reviews (MathSciNet): MR13:640h
- [11] Georges Polya, Sur une interpretation de la methode des differences finies qui peut fournir des bornes superieures ou inferieures,C. R. Acad. Sci. Paris 235 (1952), 995-997.
- [12] Georges Polya, Estimates for eigenvalues, typescript, 1952. To appear in a von Mises "Festschrift."Mathematical Reviews (MathSciNet): MR16:482b
- [13] G. Polyaand G. Szego, Isoperimetric inequalitiesin mathematicalphysics, Annals of Mathematics Studies, No. 27, Princeton University Press, 1951.
- [14] Mario G. Salvadori, Numerical computation of buckling loads by finitedifferences, Trans. Amer. Soc. Civil Engrs. 116(1951), 590-636.
- [15] G. Temple, The computation of characteristic numbers and characteristicfunc- tions, Proc. London Math. Soc. (2 ) 29 (1929), 257-280.
- [16] G. Temple, The accuracy of Rayleighfsmethod of calculating the natural fre- quencies of vibrating systems, Proc. Roy. Soc. London. Ser. A. 211(1952), 204-224.
- [17] D.H. Weinstein, Modified Ritz method, Proc. Nat. Acad. Sci. U.S.A. 20 (1934), 529-532.Zentralblatt MATH: 0010.16901
- [18] Helmut Wielandt, Die Einschliessungvon Eigenwerten normaler Matrizen, Math. Ann. 121 (1949), 234-241. NATIONAL BUREAU OF STANDARDS, LOS ANGELES (Now with the University of California, Los Angeles)
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