Proyecciones
Vol. 24, No 1, pp. 49-63, May 2005.
Universidad Católica del Norte
Antofagasta - Chile

SPECTRAL PROPERTIES OF A NON SELFADJOINT SYSTEM OF DIFFERENTIAL EQUATIONS WITH A SPECTRAL PARAMETER IN THE BOUNDARY CONDITION

E. KIR a., G. BASCANBAZ-TUNCA b. C. YANIK c.

a. Gazi University, Turkey.
b. Ankara University, Turkey.
c. Hacettepe University, Turkey.

Correspondencia a :

ABSTRACT

Key Words : Spectrum, Spectral Singularities, Non-Selfadjoint System of Di.erential Equations.

AMS Subject Classification : 34L05 (34B05 47E05 34L40).

References

[1] O. Akýn and E. Bairamov, On the structure of discrete spectrum of the non-selfadjoint system of di.erential equations in the first order, J. Korean Math. Soc. No 3, 32, pp. 401-413, (1995).        [ Links ]

[2] Yu. M. Berezanski, Expansion in Eigenfunctions of Selfadjoint Operators, Amer. Math. Soc., Providence R. I. (1968).         [ Links ]

[3] E. P. Dolzhenko, Boundary Value Uniqueness Theorems for Analytic Functions, Math. Notes 25 No 6, pp. 437-442, (1979).        [ Links ]

[4] N. B. Kerimov, A Boundary Value Problem for the Dirac System with a Spectral Parameter in the Boundary Conditions, Di.erential Equations, Vol. 38, No 2, pp. 164-174, (2002).        [ Links ]

[5] E. Kýr, Spectral Properties of Non-Selfadjoint System of Di.erential Equations, Commun. Fac. Sci. Univ. Ank. Series A1, Vol.49 (2000),111-116.        [ Links ]

[6] V.E. Lyance, A di.erential Operator with Spectral Singularities, I,II,Amer. Math. Soc.Trans. Ser. 2, Vol. 60, pp. 185-225, pp. 227-283,(1967).        [ Links ]

[7] M.A.Naimark, Investigation of the Spectrum and the Expansion in Eigenfunctions of a Non-selfadjoint Operator of Second Order on a Semi-axis, Amer. Math. Soc. Trans. Ser. 2, Vol 16, pp.103-193, Amer. Math. Soc., Providence, (1960).        [ Links ]

[8] J.T.Schwartz, Some non-selfadjoint operators, Comm. Pure and Appl.Math. 13, pp. 609-639, (1960).        [ Links ]

Received : October 2004, Accepted : April 2005.

Esra Kir
Faculty of Art and Science
06500, Teknikokullar
Ankara
Turkey
e-mail : esrakir@gazi.edu.tr

Gülen Ba¸scanbaz-Tunca
Department of mathematics
Faculty of science
Ankara University
06100, Tandogan, ankara
Turkey
e-mail: tunca@science.ankara.edu.tr

and

Canan Yanik
Department of Mathematics Education
Hacettepe University
06532 Beytepe
Ankara
Turkey
e-mail : canany@hacettepe.edu.tr