The zeta-function of a degenerate elliptic operator
Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 209-230 Cet article a éte moissonné depuis la source Math-Net.Ru

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The author constructs the meromorphic continuation to the entire complex plane of the zeta-function of the operator of a boundary value problem for an elliptic equation in divergence form, degenerating like a power at the boundary. Bibliography: 19 titles.
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A. I. Karol'. The zeta-function of a degenerate elliptic operator. Sbornik. Mathematics, Tome 52 (1985) no. 1, pp. 209-230. http://geodesic.mathdoc.fr/item/SM_1985_52_1_a11/

[1] Berger G., “Asimptotika spektra s otsenkoi ostatka ellipticheskikh operatorov so slabym vyrozhdeniem”, Vestn. LGU, 1979, no. 7, 14–19 | MR | Zbl

[2] Birman M. Sh., Solomyak M. Z., “Asimptotika spektra differentsialnykh uravnenii”, Itogi nauki i tekhniki. Matematicheskii analiz, 14, VINITI, M., 1977, 5–58 | MR

[3] Vishik M. I., Trushin V. V., “Kraevye zadachi dlya ellipticheskikh uravnenii, vyrozhdayuschikhsya na granitse oblasti”, Matem. sb., 80 (122) (1969), 455–491 | Zbl

[4] Vulis I. L., “Spektralnaya asimptotika ellipticheskikh operatorov proizvolnogo poryadka s silnym vyrozhdeniem”, Kraevye zadachi matem. fiziki i smezhnye voprosy teorii funktsii. 59, Zapiski nauchn. sem. LOMI, 1976, 25–30 | MR | Zbl

[5] Karol A. I., “O $\zeta$-funktsii vyrozhdayuscheisya ellipticheskoi kraevoi zadachi Dirikhle”, DAN SSSR, 260:1 (1981), 20–22 | MR | Zbl

[6] Karol A. I., “Operatornoznachnye PDO i rezolventa vyrozhdayuschegosya ellipticheskogo operatora”, Matem. sb., 121(163) (1983), 562–575 | MR

[7] Karol A. I., “O regulyarnosti reshenii vyrozhdayuschikhsya ellipticheskikh uravnenii vtorogo poryadka”, Problemy matematicheskogo analiza, vyp. 8, izd–vo LGU, L., 1981, 48–62 | MR

[8] Subkhankulov M. A., Tauberovy teoremy s ostatkom, Nauka, M., 1976 | MR

[9] Taschiyan G. M., “Ob otsenke ostatka v klassicheskoi formule spektralnoi asimptotiki dlya vyrozhdayuschikhsya ellipticheskikh uravnenii”, Problemy matematicheskogo analiza, vyp. 8, izd–vo LGU, L., 1981, 181–188

[10] Khardi, Littlvud, Polia, Neravenstva, IL, M., 1948

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

[12] Agmon S., “On kernels, eigenvalues and eigenfunctions of operators related to elliptic problems”, Comm. Pure and Appl. Math., 18:4 (1965), 627–663 | DOI | MR | Zbl

[13] Beats R., “A general calculus of pseudodifferential operators”, Duke Math. J., 42 (1975), 1–42 | DOI | MR

[14] Boltey P., Camus J., “Sur une classe d'opératours elliptique et dégénérés à une variable”, J. Math. Pures Appl., 51 (1972), 429–463 | MR

[15] Métivier G., “Comportement asymptotique des valeurs propres d'opérateurs elliptiques dégénérés”, Soc. Math. France, Astérisque 34–35, 1976, 215–249 | MR | Zbl

[16] Seeley R. T., “The resolvent of an elliptic boundary problem”, Amer. J. Math., 91:4 (1969), 889–920 | DOI | MR | Zbl

[17] Seeley R. T., “Analytic extension of the trace associated with elliptic boundary problems”, Amer. J. Math., 91:4 (1969), 963–983 | DOI | MR | Zbl

[18] Seeley R. T., “Complex powers of an elliptic operator”, Amer. Math. Soc, Proc. Symp. Pure Math., 10 (1967), 288–307 | MR | Zbl

[19] Shimakura N., “Sur les $\zeta$-founction d'Epstein pour des opérateurs elliptiques dégénérés”, Tôhoku Math. J., 26:1 (1974), 95–131 | DOI | MR | Zbl