Geodesic
Asymptotics of the eigenvalues of hypoelliptic operators on a closed manifold
Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 169-189 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article an asymptotic formula with an estimate of the remainder term is proved for the distribution function of the eigenvalues of hypoelliptic differential operators on a compact manifold without boundary. The proof is based on a method for constructing an approximate spectral projection for the operators under consideration. Bibliography: 16 titles. 
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V. I. Bezyaev. Asymptotics of the eigenvalues of hypoelliptic operators on a closed manifold. Sbornik. Mathematics, Tome 45 (1983) no. 2, pp. 169-189. http://geodesic.mathdoc.fr/item/SM_1983_45_2_a1/

[1] Tulovskii V. N., “Asimptoticheskoe raspredelenie sobstvennykh znachenii differentsialnykh operatorov s peremennymi koeffitsientami”, DAN SSSR, 206:4 (1972), 827–830 | MR | Zbl

[2] Tulovskii V. N., Shubin M. A., “Ob asimptoticheskom raspredelenii sobstvennykh znachenii psevdodifferentsialnykh operatorov v $\mathbf R^n$”, Matem. sb., 92 (134) (1973), 571–588 | MR | Zbl

[3] Feigin V. I., “Asimptoticheskoe raspredelenie sobstvennykh chisel dlya gipoellipticheskikh sistem v $\mathbf R^n$”, Matem. sb., 99 (141) (1976), 594–614 | MR | Zbl

[4] Métivier G., “Fonction spectrale et valeurs propres d'operateurs non elliptiques”, C. r. Acad. scient. Paris, 283:7 (1976), A453–A456 | MR

[5] Birman M. Sh., Solomyak M. Z., Asimptotika spektra differentsialnykh uravnenii, Itogi nauki i tekhniki. Matem. analiz, 14, VINITI, M., 1977 | MR

[6] Moscatelli V. B., Thompson M., “Distribution asymptotique des valeurs propres d'operateurs pseudo-différentiels sur des variétés compactes”, C. r. Acad. scient. Paris, 284:6 (1977), A373–A375 | MR

[7] Pham The Lai, “Theorie spectrale d'une classe d'operateurs différentiels hypoelliptiques”, Comm. part. differ. eq., 2:5 (1977), 439–497 | DOI | MR | Zbl

[8] Feigin V. I., “Novye klassy psevdodifferentsialnykh operatorov v $\mathbf R^n$ i nekotorye prilozheniya”, Tr. Mosk. matem. ob-va, 26 (1978), 155–194 | MR

[9] Andreev A. S., “Asimptotika spektra kraevykh zadach dlya gipoellipticheskikh operatorov “netselogo” poryadka”, Issledovaniya po teorii funktsii mnogikh veschestvennykh peremennykh, Mezhvuzov. tematich. sb., vyp. 2, YarGU, Yaroslavl, 1978, 3–14 | MR | Zbl

[10] Bezyaev V. I., “Asimptotika plotnosti sostoyanii gipoellipticheskikh pochti-periodicheskikh operatorov”, Matem. sb., 105 (147) (1978), 485–511 | Zbl

[11] Boimatov K. X., “Psevdodifferentsialnye operatory s operatornym simvolom”, DAN SSSR, 244:1 (1979), 20–24 | MR

[12] Khërmander L., “Psevdodifferentsialnye, operatory i gipoellipticheskie uravneniya”, Psevdodifferentsialnye operatory, Mir, M., 1967, 297–366

[13] Khërmander L., “Integralnye operatory Fure. I”, Matematika, 16:1 (1972), 17–61

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

[15] Bezyaev V. I., “Asimptotika sobstvennykh znachenii gipoellipticheskikh operatorov na zamknutom mnogoobrazii”, DAN SSSR, 244:5 (1979), 1054–1057 | MR | Zbl

[16] Kumano-go H., “Algebras of pseudo-differential operators”, J. Fac. Sci. Univ. Tokyo, Sec. 1A, 17:1–2 (1970), 31–50 | MR | Zbl