Voir la notice de l'article provenant de la source Math-Net.Ru
@article{FAA_1983_17_3_a4, author = {G. S. Popov and M. A. Shubin}, title = {Asymptotic expansion of the spectral function for second-order elliptic operators in $\mathbb{R}^n$}, journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a}, pages = {37--45}, publisher = {mathdoc}, volume = {17}, number = {3}, year = {1983}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FAA_1983_17_3_a4/} }
TY - JOUR AU - G. S. Popov AU - M. A. Shubin TI - Asymptotic expansion of the spectral function for second-order elliptic operators in $\mathbb{R}^n$ JO - Funkcionalʹnyj analiz i ego priloženiâ PY - 1983 SP - 37 EP - 45 VL - 17 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FAA_1983_17_3_a4/ LA - ru ID - FAA_1983_17_3_a4 ER -
%0 Journal Article %A G. S. Popov %A M. A. Shubin %T Asymptotic expansion of the spectral function for second-order elliptic operators in $\mathbb{R}^n$ %J Funkcionalʹnyj analiz i ego priloženiâ %D 1983 %P 37-45 %V 17 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/FAA_1983_17_3_a4/ %G ru %F FAA_1983_17_3_a4
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