An asymptotic formula for the number of eigenvalues of a differential operator

  • E. Adiguzelov Yildiz Technical University.
  • H. Avci Yildiz Technical University.
  • E. Gul Yildiz Technical University.


In this work, it is proved that the spectrum of an differential operator with unbounded operator coefficients in elliptic type with partial derivatives is pure discrete and an asymptotic formula is found for the number of eigenvalues of this operator.

Biografía del autor

E. Adiguzelov, Yildiz Technical University.
Department of Mathematics.
H. Avci, Yildiz Technical University.
Department of Mathematics.
E. Gul, Yildiz Technical University.
Department of Mathematics.


[1] Kostyuchenko, A. G., and Levitan, B. M., ”Asymptotic behavior of the eigenvalues of the Sturm-Liouville operator problem”, Funct. Anal. Appl. 1, pp. 75-83, (1967).

[2] Gorbauuk, M.L., ” Self adjoint boundary value problems of second order differential equation with unbounded operator coeffi- cients”, Funks. analiz i yego pril., 5, No:1, pp. 10-21, (1971).

[3] Gorbacuk, V.I., Gorbacuk, M.L., ”On a class boundary value problems for Sturm-Liouville equation with operator coefficients”, Ukr. mat. jur., T.24, No:3, pp. 291-305, (1972).

[4] Gorbacuk, V. I., Gorbacuk, M. L., ” Some problems of spectral theory of differential equations in elliptic type in space of vector functions”, Ukr. mat. jur., T.28, No:3, pp. 313-324, (1976).

[5] Otelbayev, M., ”On Titcmars method of restriction of resolvent”, Dokl. A.N. SSSR, T.281, No:4, pp. 787-790, (1973).

[6] Solomyak, M. Z., ”Asymptotics of the spectrum of the Schrodinger operator with non-regular homogeneous potential”, Math. USSR Sbornik, Vol. 55, No:1, pp. 19-37, (1986).

[7] Maksudov, F. G., Bairamoglu, M., Adiguzelov,E. E., ”On asymptotics of spectrum and trace of high order differential operator with operator coefficients”, Doa Turkish Journal of mathematics, vol. 17, number 2, 1993, 113-128

[8] Kirillov, A. A., Elementary theory of representations, Springer verlag, New York, (1976).

[9] Cohberg,. C., and Krein, M. G., ”Introduction to the theory of linear non-self adjoint operators”, Translation of Mathematical Monographs volume 18, Amer. Math. Sos., Providence, R. I. (1969).

[10] Eydelman, S. D., ”Parabolic Systems”, North-Holland Publishing Company Amsterdam, (1969).

[11] Kostyuchenko, A. G., ”The asymptotic behavior of the spectral function of self adjoint operators in elliptic type”, V kn ”Cetvyontaya matem. skola” , Kiev, pp. 42-117, (1968).

[12] Korenblyum, B. I., ”General Tauber Teorems for the ration of functions”, DAN SSSR , 88 No:5, pp. 745-748, (1953).
Cómo citar
Adiguzelov, E., Avci, H., & Gul, E. (2017). An asymptotic formula for the number of eigenvalues of a differential operator. Proyecciones. Revista De Matemática, 20(1), 65-82.