Asymptotic expansion of the spectral function for second-order elliptic operators in $\mathbb{R}^n$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 17 (1983) no. 3, pp. 37-45.

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G. S. Popov; M. A. Shubin. Asymptotic expansion of the spectral function for second-order elliptic operators in $\mathbb{R}^n$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 17 (1983) no. 3, pp. 37-45. http://geodesic.mathdoc.fr/item/FAA_1983_17_3_a4/

[1] Buslaev V.S., “Ob asimptoticheskom povedenii spektralnykh kharakteristik vneshnikh zadach dlya operatora Shredingera”, Izv. AN SSSR, seriya matem., 39:1 (1975), 149–235 | MR | Zbl

[2] Arsenev A.A., “Asimptotika spektralnoi funktsii uravneniya Shredingera”, Zhurnal vychisl. matem. i matem. fiz., 7:6 (1967), 507–518 | MR

[3] Vainberg B.R., “O korotkovolnovoi asimptotike reshenii statsionarnykh zadach i asimptotike pri $t\to\infty$ reshenii nestatsionarnykh zadach”, UMN, 30:2 (1975), 3–55 | MR | Zbl

[4] Buslaev V.S., “Rasseyannye ploskie volny, spektralnye asimptotiki i formuly sleda dlya vneshnikh zadach”, DAN SSSR, 197:5 (1971), 999–1002 | MR | Zbl

[5] Majda A., Ralston J., “An analogue of Weyl's formula for unbounded domains, I, II, III”, Duke Math. J., 45:1 (1978), 183–196 ; 3, 513–536 ; 46:4 (1979), 725–731 | DOI | MR | Zbl | MR | Zbl | DOI | MR | Zbl

[6] Petkov V., Popov G., “Asymptotic behaviour of the scattering phase for non-trapping obstacles”, Ann. Inst. Fourier, 32:3 (1982), 111–150 | DOI | MR

[7] Ivrii V.Ya., Shubin M.A., “Ob asimptotike funktsii spektralnogo sdviga”, DAN SSSR, 263:2 (1982), 283–284 | MR

[8] Hörmander L., “The spectral function of an elliptic operator”, Acta Math., 121:3–4 (1968), 193–218 | DOI | MR | Zbl

[9] Rauch J., “Asymptotic behaviour of solutions to hyperbolic differential equations with zero speeds”, Comm. Pure Appl. Math., 31:4 (1978), 431–480 | DOI | MR | Zbl

[10] Duistermaat J., Hörmander L., “Fourier integral operators II”, Acta Math., 128:3–4 (1972), 183–269 | DOI | MR | Zbl

[11] Kuroda S., “Scattering theory for differential operators. I. Operator theory. II. Self-adjoint elliptic operators”, J. Math. Soc. Japan, 25:1 (1973), 75–104 ; 4, 222–234 | DOI | MR | Zbl | MR | Zbl

[12] Rid M., Saimon B., Metody sovremennoi matematicheskoi fiziki. T. 1. Funktsionalnyi analiz, Mir, M., 1977 ; Методы современной математической физики. Т. 4. Анализ операторов, Мир, М., 1982 | MR | MR

[13] McKean H., Singer I., “Curvature and the eigenvalues of the Laplacian”, J. Differential Geometry, 1:4 (1967), 43–69 | MR | Zbl

[14] Duistermaat J., Guillemin V., “The spectrum of positive elliptic operators and periodic bi characteristics”, Invent. Math., 29:1 (1975), 39–79 | DOI | MR | Zbl

[15] Giiemin V., Sternberg S., Geometricheskie asimptotiki, Mir., M., 1981 | MR

[16] Shubin M.A., Psevdodifferentsialnye operatory i spektralnaya teoriya, Nauka, M., 1978 | MR

[17] Babich V.M., “O korotkovolnovoi asimptotike resheniya zadachi o tochechnom istochnike v neodnorodnoi srede”, Zhurnal vychisl. matem. i matem. fiz., 5:5 (1965), 949–951 | Zbl

[18] Kucherenko V.V., “Kvaziklassicheskaya asimptotika funktsii tochechnogo istochnika dlya statsionarnogo uravneniya Shredingera”, Teor. i matem. fizika, 1:3 (1969), 384–406 | MR

[19] Kucherenko V.V., “Nekotorye svoistva korotkovolnovoi asimptotiki fundamentalnogo resheniya uravneniya $[\Delta+k^2n(x)]u=0$”, Asimptoticheskie metody i raznostnye skhemy, Trudy MIEM, 25, M., 1972

[20] Babich V.M., Rapoport Yu.O., “Asimptotika pri malykh vremenakh fundamentalnogo resheniya zadachi Koshi dlya parabolicheskogo uravneniya vtorogo poryadka”, Problemy matem. fiziki, 7, Izd. Leningr. un-ta, L., 1974, 21–38

[21] Babich V.M., “Metod Adamara i asimptotika spektralnoi funktsii differentsialnogo operatora vtorogo poryadka”, Matem. zametki, 28:5 (1980), 689–694 | MR | Zbl

[22] Popov G.S., Shubin M.A., “Polnoe asimptoticheskoe razlozhenie spektralnoi funktsii dlya ellipticheskikh operatorov vtorogo poryadka v $\mathbf R^n$”, UMN, 38:1 (1983), 187–188 | MR | Zbl