Asymptotic of the spectral function of a positive elliptic operator without the nontrap condition
Funkcionalʹnyj analiz i ego priloženiâ, Tome 22 (1988) no. 3, pp. 53-65.

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Yu. G. Safarov. Asymptotic of the spectral function of a positive elliptic operator without the nontrap condition. Funkcionalʹnyj analiz i ego priloženiâ, Tome 22 (1988) no. 3, pp. 53-65. http://geodesic.mathdoc.fr/item/FAA_1988_22_3_a4/

[1] Levitan B.M., “Ob asimptoticheskom povedenii spektralnoi funktsii samosopryazhennogo differentsialnogo uravneniya vtorogo poryadka”, Izv. AN SSSR. Ser. mat., 16:4 (1952), 325–352 | MR | Zbl

[2] Hörmander L., “On the Riesz means of spectral functions and eigenfunction expansions for elliptic differential operators”, Recent Advances in the Basic Sciences, Yeshiva Univ. Conference, Nov., 1966, 155–202 | MR

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

[4] Levitan B.M., “Asimptoticheskoe povedenie spektralnoi funktsii ellipticheskogo uravneniya”, UMN, 26:6 (1971), 151–212 | MR | Zbl

[5] Buslaev V.S., “Rasseyannye ploskie volny, spektralnye asimptotiki i formuly sleda vo vneshnikh zadachakh/”, AN SSSR, 197:5 (1971), 999–1002 | MR | Zbl

[6] Buslaev B.C., “Ob asimptoticheskom povedenii spektralnykh kharakteristik vneshnikh zadach dlya operatora Shredingera”, Izv. AN SSSR. Ser. mat., 39:1 (1975), 149–235 | MR | Zbl

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

[8] Babich B.M., Levitan B.M., “Zadacha o fokusirovke i asimptotika spektralnoi funktsii operatora Laplasa–Beltrami”, Zap. nauch. sem. LOMI, 78, 1978, 3–19 | MR | Zbl

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

[10] Ivrii V.Ya., “O tochnykh spektralnykh asimptotikakh dlya ellipticheskikh operatorov, deistvuyuschikh v rassloeniyakh”, Funktsion. analiz i ego pril., 16:2 (1982), 30–38 | MR | Zbl

[11] Popov G.S., Shubin M.A., “Asimptoticheskoe razlozhenie spektralnoi funktsii dlya ellipticheskikh operatorov vtorogo poryadka v $\mathbf R^n$”, Funktsion. analiz i ego pril., 17:3 (1983), 37–45 | MR | Zbl

[12] Ivrii V.Ja., “Precise spectral asymptotics for elliptic operators acting in fiberings over manifolds with boundary”, Lecture Notes in Math., 1100, Springer-Verlag, 1984 | DOI | MR | Zbl

[13] Vainberg B.P., “Parametriks i asimptotika spektralnoi funktsii differentsialnykh operatorov v $\mathbf R^n$”, Mat. sbornik, 130:2 (1986), 243–264 | MR

[14] Safarov Yu.G., “Asimptotika spektra psevdodifferentsialnogo operatora s periodicheskimi bikharakteristikami”, Zap. nauch. sem. LOMI, 152, 1986, 94–104 | Zbl

[15] Safarov Yu.G., “Asimptotika spektra kraevoi zadachi s periodicheskimi billiardnymi traektoriyami”, Funktsion. analiz i ego pril., 21:4 (1987), 88–90 | MR | Zbl

[16] Hörmander L., “Fourier integral operators. I”, Acta Math., 127:1–2 (1971), 79–183 | DOI | MR | Zbl

[17] Tpev F., Vvedenie v teoriyu psevdo differentsialnykh operatorov i integralnykh operatorov Fure, T. 2, Mir, M., 1984

[18] Sekefalvi-Nad B., Foiash Ch., Garmonicheskii analiz operatorov v gilbertovom prostranstve, Mir, M., 1970 | MR

[19] Babich V.M.. Lazutkin V.F., “O sobstvennykh funktsiyakh, sosredotochennykh vblizi zamknutoi geodezicheskoi”, Problemy matematicheskoi fiziki, no. 2, Izd-vo LGU, L., 1967, 15–25

[20] Vasilev D.G., “Dvuchlennaya asimptotika spektra kraevoi zadachi”, Funktsion. analiz i ego pril., 17:4 (1983), 79–81 | MR

[21] Vasilev D.G., “Dvuchlennaya asimptotika spektra kraevoi zadachi pri vnutrennem otrazhenii obschego vida”, Funktsion. analiz i ego pril., 18:4 (1984), 1–13 | MR

[22] Gureev T.E., Safarov Yu.G., “Tochnaya asimptotika spektra operatora Laplasa na mnogoobrazii s periodicheskimi geodezicheskimi”, Trudy MIAN, 179, 1988, 36–53 | MR | Zbl

[23] Safarov Yu.G., “O srednikh Rissa,funktsii raspredeleniya sobstvennykh znachenii ellipticheskogo operatora”, Zap. nauch. sem. LOMI, 163, 1987, 143–145 | MR

[24] Hörmander L., The Analysis of Linear Partial Differential Operators, IV, Springer-Verlag, 1984 | MR