Year 2005, Volume 18 , Issue 2, Pages 239 - 247 2010-08-13

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

Esra KIR [1]


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 + .

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
  • Z.S. Agranovich and Marchenko V.A., The Inverse Problem of Scattering Theory, (1963).
  • M.A. Naimark., Linear Differential Operators I,II, Ungar, New-York, (1968).
  • V.E. Lyance, “A Differential Operator with Spectral Singularities I,II”, AMS Translations 2(60), 185-225, 227-283 (1960).
  • J.T. Schwartz, “ Some Non-selfadjoint Operators”, Comm.Pure and Appl.Math 13, 609-639 (1960).
  • 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
  • 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).
  • 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).
  • 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).
  • Yu. M., Brezanski, Expansion in Eigenfunctions of Selfadjoint Operators. Amer. Math. Soc., Providence R.I. (1968).
Primary Language en
Journal Section Mathematics
Authors

Author: Esra KIR

Dates

Publication Date : August 13, 2010

Bibtex @ { gujs97160, journal = {Gazi University Journal of Science}, issn = {}, eissn = {2147-1762}, address = {}, publisher = {Gazi University}, year = {2010}, volume = {18}, pages = {239 - 247}, doi = {}, title = {THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES}, key = {cite}, author = {Kır, Esra} }
APA Kır, E . (2010). THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES . Gazi University Journal of Science , 18 (2) , 239-247 . Retrieved from https://dergipark.org.tr/en/pub/gujs/issue/7414/97160
MLA Kır, E . "THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES" . Gazi University Journal of Science 18 (2010 ): 239-247 <https://dergipark.org.tr/en/pub/gujs/issue/7414/97160>
Chicago Kır, E . "THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES". Gazi University Journal of Science 18 (2010 ): 239-247
RIS TY - JOUR T1 - THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES AU - Esra Kır Y1 - 2010 PY - 2010 N1 - DO - T2 - Gazi University Journal of Science JF - Journal JO - JOR SP - 239 EP - 247 VL - 18 IS - 2 SN - -2147-1762 M3 - UR - Y2 - 2021 ER -
EndNote %0 Gazi University Journal of Science THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES %A Esra Kır %T THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES %D 2010 %J Gazi University Journal of Science %P -2147-1762 %V 18 %N 2 %R %U
ISNAD Kır, Esra . "THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES". Gazi University Journal of Science 18 / 2 (August 2010): 239-247 .
AMA Kır E . THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES. Gazi University Journal of Science. 2010; 18(2): 239-247.
Vancouver Kır E . THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES. Gazi University Journal of Science. 2010; 18(2): 239-247.
IEEE E. Kır , "THE PRINCIPAL FUNCTIONS OF THE SYSTEM OF FINITE STRUM-LIOUVILLE DIFFERENTIAL OPERATORS CORRESPONDING TO THE EIGENVALUES AND SPECTRAL SINGULARITIES", Gazi University Journal of Science, vol. 18, no. 2, pp. 239-247, Aug. 2010