×

zbMATH — the first resource for mathematics

The spectral function of an elliptic operator. (English) Zbl 0164.13201

MSC:
35P20 Asymptotic distributions of eigenvalues in context of PDEs
35S05 Pseudodifferential operators as generalizations of partial differential operators
47G30 Pseudodifferential operators
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Agmon, S. &Kannai, Y., On the asymptotic behavior of spectral functions and resolvent kernels of elliptic operators.Israel J. Math., 5 (1967), 1–30. · Zbl 0148.13003 · doi:10.1007/BF02771593
[2] Avakumovič, V. G., Über die Eigenfunktionen auf geschlossenen Riemannschen Mannigfaltigkeiten.Math. Z., 65 (1956), 327–344. · Zbl 0070.32601 · doi:10.1007/BF01473886
[3] Carleman, T., Propriétés asymptotiques des fonctions fondamentales des membranes vibrantes.C. R. Sème Congr. des Math. Scand. Stockholm 1934; 34–44 (Lund 1935).
[4] Gårding, L., On the asymptotic distribution of the eigenvalues and eigenfunctions of elliptic differential operators.Math. Scand., 1 (1953), 237–255. · Zbl 0053.39102
[5] –, On the asymptotic properties of the spectral function belonging to a self-adjoint semi-bounded extension of an elliptic differential operator.Kungl. Fysiogr. Sällsk. i Lund Förh., 24, No. 21 (1954), 1–18.
[6] Hörmander, L., Pseudo-differential operators.Comm. Pure Appl. Math., 18 (1965), 501–517. · Zbl 0125.33401 · doi:10.1002/cpa.3160180307
[7] –, Pseudo-differential operators and hypoelliptic equations.Amer. Math. Soc. Proc. Symp. Pure Math., 10 (1968), 138–183.
[8] Hörmander, L., On the Riesz means of spectral functions and eigenfunction expansions for elliptic differential operators.Recent Advances in the Basic Sciences, Yeshiva University Conference November 1966, 155–202 (to appear).
[9] Lax, P. D., Asymptotic solutions of oscillatory initial value problems.Duke Math. J., 24 (1957), 627–646. · Zbl 0083.31801 · doi:10.1215/S0012-7094-57-02471-7
[10] Lewitan, B. M., On the asymptotic behavior of the spectral function of a self-adjoint differential equation of the second order.Izv. Akad. Nauk SSSR Sér. Mat., 16 (1952), 325–352.
[11] –, On the asymptotic behavior of the spectral function and the eigenfunction expansion of self-adjoint differential equations of the second order II.Izv. Akad. Nauk SSSR Sér. Mat., 19 (1955), 33–58.
[12] Minakshisundaram, S. &Pleijel, Å., Some properties of the eigenfunctions of the Laplace operator on Riemannian manifolds.Canad. J. Math., 4 (1952), 26–30. · Zbl 0049.17103 · doi:10.4153/CJM-1952-002-4
[13] Müller, C.,Spherical harmonics. Springer-Verlag lecture notes in mathematics, 17 (1966).
[14] Seeley, R. T., Complex powers of an elliptic operator.Amer. Math. Soc. Proc. Symp. Pure Math., 10 (1968), 288–307.
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.