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Literature Cited
V. S. Buslaev, "On the asymptotic behavior of spectral characteristics of exterior problems for the Schrödinger operator," Izv. Akad. Nauk SSSR, Ser. Mat.,39, No. 1, 148–235 (1975).
A. A. Arsen'ev, "Asymptotic behavior of the spectral function of the Schrödinger equation," Zh. Vychisl. Mat. Mat. Fiz.,7, No. 6, 507–518 (1967).
B. R. Vainberg, "On the short-wave asymptotic of solutions to stationary problems and the asymptotic for t → ∞ of solutions to nonstationary problems," Usp. Mat. Nauk,30, No. 2, 1–55 (1975).
V. S. Buslaev, "Scattered plane waves, spectral asymptotics, and trace formulas for exterior problems," Dokl. Akad. Nauk SSSR,197, No. 5, 999–1002 (1971).
A. Majda and J. Ralston, "An analogue of Weyl's formula for unbounded domains. I, II, III," Duke Math. J.,45, No. 1, 183–196 (1978);45, No. 3, 513–536;46, No. 4, 725–731 (1979).
V. Petkov and G. Popov, "Asymptotic behavıor of the scattering phase for nontrapping obstacles," Ann. Inst. Fourier,32, No. 3, 111–150 (1982).
V. Ya. Ivrii and M. A. Shubin, "On the asymptotic behavior spectral shift function," Dokl. Akad. Nauk SSSR,263, No. 2, 283–284 (1982).
L. Hörmander, "The spectral function of an elliptic operator," Acta Math.,121, Nos. 3–4, 193–218 (1968).
J. Rauch, "Asymptotic behaviour of solutions to hyperbolic differential equations with zero speeds," Commun. Pure Appl. Math.,31, No. 4, 431–480 (1978).
J. Duistermaat and L. Hörmander, "Fourier integral operators. II," Acta Math.,128, Nos. 3–4, 183–269 (1972).
S. Kuroda, "Scattering theory for differential operators. I. Operator theory. II. Self-adjoint elliptic operators," J. Math. Soc. Jpn.,25, No. 1, 75–104; No. 4, 222–234 (1973).
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis, Academic Press, New York (1972).
H. McKean and I. Singer, "Curvature and the eigenvalues of the Laplacian," J. Diff. Geom.,1, No. 4, 43–69 (1967).
J. Duistermaat and V. Guillemin, "The spectrum of positive elliptic operators and periodic bicharacteristics," Invent. Math.,29, No. 1, 39–79 (1975).
V. Guillemin and S. Sternberg, Geometric Asymptotics, Math. Surveys, No. 14, Amer. Math. Soc., Providence, Rhode Island (1977).
M. A. Shubin, Pseudodifferential Operators and Spectral Theory [in Russian], Nauka, Moscow (1978).
V. M. Babich, "On the short-wave asymptotic of the solution to the point-source problem in a nonhomogeneous medium," Zh. Vychisl. Mat. Mat. Fiz.,5, No. 5, 949–951 (1965).
V. V. Kucherenko. "Quasiclassical asymptotics of the point-source function for the stationary Schrödinger equation," Theor. Mat. Fiz.,1, No. 3, 384–406 (1969).
V. V. Kucherenko, "Some properties of the short-wave asymptotic of the fundamental solution of the equation [Δ + k2n(x)]u = 0," in: Trudy MIÉM, Asymptotic Methods and Difference Schemes, Vol. 25, Moscow (1972).
V. M. Babich and Yu. O. Rapoport, "Short-time asymptotic of the fundamental solution to the Cauchy problem for a second-order parabolic equation," in: Problems of Mathematical Physics, No. 7, Leningrad State Univ. (1974), pp. 21–38.
V. M. Babich, "Hadamard's method and the asymptotic of the spectral function of a secondorder differential operator," Mat. Zametki,28, No. 5, 689–694 (1980).
G. S. Popov and M. A. Shubin, "Complete asymptotic expansion of the spectral function for second-order elliptic operators in Rn," Usp. Mat. Nauk,38, No. 1, 187–188 (1983).
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Mathematics and Mechanics Institute, Bulgarian Academy of Sciences. Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 17, No. 3, pp. 37–45, July–September, 1983.
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Popov, G.S., Shubin, M.A. Asymptotic expansion of the spectral function for second-order elliptic operators in Rn . Funct Anal Its Appl 17, 193–200 (1983). https://doi.org/10.1007/BF01078101
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DOI: https://doi.org/10.1007/BF01078101