THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES

Abstract

ABSTRACT

In this paper, the principal functions of the system of finite Sturm-Liouville differential operators corresponding to the eigenvalues and spectral singularities are investigated. We have proved that the principal functions of L corresponding to the eigenvalues are in ( , ) 2 L R C N + and the principal functions corresponding to the spectral singularities are in another Hilbert space which contains ( , ) 2 L R C N + .

Keywords

• Key Words: Eigen-values, spectral singularities, principal function

SPECTRAL SINGULARITIES

Abstract

Bu çalışmada sonlu Sturm-Liouville diferensiyel operatörler sisteminin özdeğerlerine ve spektral tekilliklerine karşılık gelen esas fonksiyonlar incelenmiştir. Özdeğerlerine karşılık gelen esas fonksiyonların Luzayına, spektral tekilliklere karşılık gelen esas fonksiyonların Luzayını içeren bir başka Hilbert uzaya ait olduğu ispatlanmıştır

Keywords

• Özdeğer, spektral tekillik, esas fonksiyon

References

1. Z.S. Agranovich and Marchenko V.A., The Inverse Problem of Scattering Theory, (1963).
2. M.A. Naimark., Linear Differential Operators I,II, Ungar, New-York, (1968).
3. V.E. Lyance, “A Differential Operator with Spectral Singularities I,II”, AMS Translations 2(60), 185-225, 227-283 (1960).
4. J.T. Schwartz, “ Some Non-selfadjoint Operators”, Comm.Pure and Appl.Math 13, 609-639 (1960).
5. E. Bayramov and E. Kır,” Spectral Properties of a Finite System of Sturm-Liouville Differential Operators” Indian J. Pure and Appl.Math.35(2), 249-256. 2004
6. E. Bairamov, Ö. Çakar and A.O. Çelebi, “ Quadratic Pencil of Schrödinger Operators with Spectral Singularities: Discrete Spectrum and Principal Functions”, J.Math.Anal.Appl. 216, 303-320 (1997).
7. E. Bairamov, Ö. Çakar, and A.M.Krall, “ Spectrum anad Spectral Singularities of a Quadratic Pencil of a Schrödinger Operator with a General Boundary Condition” J. Differential Equations 151, 252-267 (1999).
8. E.Bairamov, Ö. Çakar and C. Yanık, “ Spectral Singularities of the Klein-Gordon s- wave Equation” Indian J. Pure appl. Math,32, 851-857 (2001).

9. Yu. M., Brezanski, Expansion in Eigenfunctions of Selfadjoint Operators. Amer. Math. Soc., Providence R.I. (1968).