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Asymptotic expansion of the spectral function of elliptic operators in \({\mathbb{R}}^ n\). (English. Russian original) Zbl 0713.47046

J. Sov. Math. 47, No. 3, 2537-2546 (1989); translation from Tr. Semin. Im. I. G. Petrovskogo 12, 75-87 (1987).
See the review in Zbl 0682.47027.

MSC:

47F05 General theory of partial differential operators
47A10 Spectrum, resolvent
58J50 Spectral problems; spectral geometry; scattering theory on manifolds

Citations:

Zbl 0682.47027
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Full Text: DOI

References:

[1] B. R. Vainberg, ?The complete asymptotic expansion of the spectral function of elliptic operators inR n ,? Vestn. Mosk. Univ. Mat. Mekh., No. 3, 29?36 (1983).
[2] B. R. Vainberg, ?The complete asymptotic expansion of the spectral function of second-order elliptic operators inR n ,? Mat. Sb.,123(165), No. 2, 195?211 (1984).
[3] V. S. Buslaev, ?Diffused planar waves, spectral asymptotics and trace formulas in exterior problems,? Dokl. Akad. Nauk SSSR,197, No. 5, 999?1002 (1971). · Zbl 0224.47023
[4] V. S. Buslaev, ?Asymptotic behavior of spectral characters of exterior problems for the Schrödinger operator,? Izv. Akad. Nauk SSSR, Ser. Mat. Mekh.,39, No. 1, 149?235 (1975).
[5] V. M. Babich, ?Short wave asymptotics of a solution to the problem of point source in a homogeneous medium,? Zh. Vychisl. Mat. Mat. Fiz.,5, No. 5, 949?951 (1965).
[6] V. V. Kucherenko, ?Quasiclassical asymptotics of a function of a point source for a stationary Schrödinger’s equation,? Teor. Mat. Fiz.,1, No. 3, 384?406 (1969). · doi:10.1007/BF01035745
[7] G. S. Popov and M. A. Shubin, ?Asymptotic expansion of a spectral function for second-order elliptic operators inR n ,? Funkts. Anal. Prilozhen.,17, No. 3, 37?45 (1983).
[8] G. S. Popov, ?Spectral asymptotics for second order differential operators,? Dokl. Bolg. Akad. Nauk,36, No. 4, 413?415 (1983).
[9] V. M. Babich, ?Hadamard’s method and asymptotics of a spectral function of a second-order differential operator,? Mat. Zametki,28, No. 5, 689?694 (1980). · Zbl 0463.35060
[10] B. R. Vainberg, Asymptotic Methods in Equations of Mathematical Physics [in Russian], Moscow State Univ. (1982).
[11] B. R. Vainberg, ?Parametrix and asymptotics of a spectral function of differential operators inR n ,? Mat. Sb.,330(172), No. 2, 243?264 (1986).
[12] V. P. Maslov and M. V. Fedoryuk, Quasiclassical Approximation for Equations of Quantum Mechanics [in Russian], Nauka, Moscow (1976). · Zbl 0449.58002
[13] A. S. Mishchenko, B. Yu. Sternin, and V. E. Shatalov, Lagrangian Manifolds and the Method of the Canonical Operator [in Russian], Nauka, Moscow (1978). · Zbl 0437.58007
[14] B. R. Vainberg, ?Parametrix and asymptotics of a spectral function of differential operators inR n ,? Dokl. Akad. Nauk SSSR,282, No. 2, 265?269 (1985).
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