Geodesic
Asymptotic distribution of eigenvalues for hypoelliptic systems in $R^n$
Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 533-552 
V. I. Feigin. Asymptotic distribution of eigenvalues for hypoelliptic systems in $R^n$. Sbornik. Mathematics, Tome 28 (1976) no. 4, pp. 533-552. http://geodesic.mathdoc.fr/item/SM_1976_28_4_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

General symmetric hypoelliptic systems of differential operators in $R^n$ with discrete spectrum are considered. Two-sided estimates, as $t\to\infty$, are found for $N(t)$, the number of eigenvalues in the interval $[0,t]$. Under a regularity assumption on the behavior of the spectrum of the Weyl matrix symbol of the system, these estimates reduce to the asymptotics of $N(t)$ with an estimate of the remainder term. In part the results are also new for the scalar case. Bibliography: 9 titles.

[1] E. Ch. Titchmarsh, Razlozheniya po sobstvennym funktsiyam, svyazannye s differentsialnymi uravneniyami vtorogo poryadka, t. 2, IL, Moskva, 1961

[2] A. G. Kostyuchenko, Doktorskaya dissertatsiya, MGU, Moskva, 1966

[3] M. Sh. Birman, V. V. Borzov, “Ob asimptotike diskretnogo spektra nekotorykh singulyarnykh operatorov”, Problemy matem. fiziki, izd-vo LGU, Leningrad, 1971, 24–37 | MR

[4] G. V. Rozenblyum, “Asimptotika sobstvennykh chisel operatora Shredingera”, Matem. sb., 93 (135) (1974), 347–367

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

[6] V. I. Feigin, “Novye klassy psevdodifferentsialnykh operatorov v $R^n$ i nekotorye prilozheniya”, Trudy Mosk. matem. ob-va, XXXVI (1976)

[7] S. A. Smagin, Kandidatskaya dissertatsiya, MGU, Moskva, 1975

[8] R. S. Ismagilov, “Ob asimptotike spektra differentsialnykh operatorov v prostranstve vektor-funktsii”, Matem. zametki, 9:6 (1971), 667–676 | MR | Zbl

[9] V. I. Feigin, “Dve algebry psevdodifferentsialnykh operatorov v $R^n$ i nekotorye prilozheniya”, Uspekhi matem. nauk, XXXI:2(188) (1976), 233–234 | MR | Zbl