×

A note on a formula of Gelfand and Levitan. (English) Zbl 0288.34020


MSC:

34L99 Ordinary differential operators
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gelfand, I. M.; Levitan, B. M., On a simple identity for the characteristic values of a differential operator of the second order (Russian), Dokl. Akad. Nauk SSSR, 88, 593-596 (1953)
[2] Halberg, C. J.A.; Kramer, V. A., A generalization of the trace concept, Duke Math. J., 27, 607-617 (1960) · Zbl 0095.09502
[3] Dikii, L. A., On a formula of Gelfand-Levitan (Russian), Uspehi Mat. Nauk, 8, 119-123 (1953)
[4] Gasymov, M. G., The sum of differences of eigenvalues of two self-adjoint operators, Soviet Math. Dokl., 4, 838-842 (1963) · Zbl 0191.15102
[5] Minakshisundaram, S.; Pleijel, A., Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds, Can. J. Math., 1, 242-256 (1949) · Zbl 0041.42701
[6] Minakshisundaram, S., A generalization of Epstein zeta function, Can. J. Math., 1, 320-327 (1949) · Zbl 0034.05103
[7] Kac, M., Can one hear the shape of a drum?, Amer. Math. Monthly, 73, 1-23 (1966) · Zbl 0139.05603
[8] McKean, H. P.; Singer, I. M., Curvature and the eigenvalues of the Laplacian, J. Diff. Geom., 1, 43-69 (1967) · Zbl 0198.44301
[9] Stewartson, K.; Waechter, R. T., On hearing the shape of a drum: Further results, (Proc. Camb. Phil. Soc., 69 (1971)), 353-363 · Zbl 0219.73088
[10] Greiner, P., An asymptotic expansion for the heat equation, Arch. Rat. Mech. Anal., 41, 163-218 (1971) · Zbl 0238.35038
[11] Friedman, A., Partial Differential Equations of Parabolic Type (1964), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0144.34903
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.