Asymptotic formulas with remainder estimates for eigenvalues of elliptic operators. (English) Zbl 0159.15903


35Pxx Spectral theory and eigenvalue problems for partial differential equations
35Jxx Elliptic equations and elliptic systems
Full Text: DOI


[1] Agmon, S., On the asymptotic distribution of eigenvalues of differential problems. Seminari dell’Istituto Nazionale di Alta Matematica 1962–63. Roma: Edizioni Cremonese 1964. 556–573.
[2] Agmon, S., Lectures on Elliptic Boundary Value Problems. Princeton, N.J.: Van Nostrand Mathematical Studies 1965. · Zbl 0142.37401
[3] Agmon, S., On kernels, eigenvalues, and eigenfunctions of operators related to elliptic problems. Comm. Pure Appl. Math. 18, 627–663 (1965). · Zbl 0151.20203
[4] Agmon, S., & Y. Kannai, On the asymptotic behavior of spectral functions and resolvent kernels of elliptic operators. Israel J. Math. 5, 1–30 (1967). · Zbl 0148.13003
[5] Avakumovic, V. G., Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten. Math. Z. 65, 327–344 (1956). · Zbl 0070.32601
[6] Bergendal, G., Convergence and summability of eigenfunction expansions connected with elliptic differential operators. Med. Lunds Univ. Mat. Sem. 15, 1–63 (1959). · Zbl 0093.06901
[7] Browder, F. E., Le problème des vibrations pour un operateur aux dérivées partielles self-adjoint et du type elliptique à coefficients variables. C. R. Acad. Sci. Paris 236, 2140–2142 (1953). · Zbl 0051.32802
[8] Browder, F. E., The asymptotic distribution of eigenfunctions and eigenvalues for semi-elliptic differential operators. Proc. Nat. Acad. Sci. U.S.A. 43, 270–273 (1957). · Zbl 0077.30002
[9] Browder, F. E., Asymptotic distribution of eigenvalues and eigenfunctions for non-local elliptic boundary value problems I. Amer. J. Math. 87, 175–195 (1965). · Zbl 0143.14403
[10] Carleman, T., Propriétés asymptotiques des fonctions fondamentales des membranes vibrantes. C. R. du 8ème Congrès des Math. Scand. Stockholm 1934 (Lund 1935), 34–44.
[11] Courant, R., & D. Hilbert, Methods of Mathematical Physics I. New York: Interscience 1953 · Zbl 0051.28802
[12] Ehrling, G., On a type of eigenvalue problems for certain elliptic differential operators. Math. Scand. 2, 267–285 (1954). · Zbl 0056.32304
[13] Gårding, L., On the asymptotic distribution of the eigenvalues and eigenfunctions of elliptic differential operators. Math. Scand. 1, 237–255 (1953). · Zbl 0053.39102
[14] Gårding, L., Eigenfunction expansions connected with elliptic differential operators. C. R. du 12ème Congrès des Math. Scand. (Lund 1953), 44–55.
[15] Gårding, L., On the asymptotic properties of the spectral function belonging to a selfadjoint semi-bounded extension of an elliptic differential operator. Kungl. Fysiogr. Sällsk. i Lund Forth. 24, 1–18 (1954). · Zbl 0058.08802
[16] Hörmander, L., On the Riesz means of spectral functions and eigenfunction expansions for elliptic differential operators. (To appear.)
[17] Malliavin, P., Un théorème taubérien avec reste pour la transformée de Stieltjes. C. R. Acad. Sci. 255, 2351–2352 (1962). · Zbl 0109.33401
[18] Mizohata, S., Sur les propriétés asymptotiques des valeurs propres pour les opérateurs elliptiques. J. Math. Kyoto Univ. 4, 399–428 (1965). · Zbl 0147.09602
[19] Mizohata, S., & R. Arima, Propriétés asymptotiques des valeurs des opérateurs elliptiques auto-adjoints. J. Math. Kyoto Univ. 4, 245–254 (1964). · Zbl 0137.30102
[20] Pleijel, Å., On a theorem by P. Malliavin. Israel J. Math. 1, 166–168 (1963). · Zbl 0126.11503
[21] Weyl, H., Die asymptotische Verteilungsgesetze der Eigenwerte linearer partieller Differentialgleichungen. Math. Ann. 71, 441–479 (1912). · JFM 43.0436.01
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.