In this paper, we consider the discrete SturmLiouville operator generated by second order difference equation with nonselfadjoint operator coefficient. This operator is the discrete analogue of the SturmLiouville differential operator generated by SturmLiouville operator equation which has been studied in detail. We find the Jost solution of this operator and examine its asymptotic and analytical properties. Then, we find the continuous spectrum, the point spectrum and the set of spectral singularities of this discrete operator. We finally prove that this operator has a finite number of eigenvalues and spectral singularities under a specific condition.
Primary Language  en 

Subjects  Mathematics 
Published Date  June2020 
Journal Section  Research Articles 
Authors 

Dates 
Application Date
: October 1, 2019

Bibtex  @research article { saufenbilder627496,
journal = {Sakarya University Journal of Science},
issn = {},
eissn = {2147835X},
address = {},
publisher = {Sakarya University},
year = {2020},
volume = {24},
pages = {494  500},
doi = {10.16984/saufenbilder.627496},
title = {Spectral Analysis of Nonselfadjoint Second Order Difference Equation with Operator Coefficient},
key = {cite},
author = {Mutlu, Gökhan and Kır Arpat, Esra}
} 
APA  Mutlu, G , Kır Arpat, E . (2020). Spectral Analysis of Nonselfadjoint Second Order Difference Equation with Operator Coefficient . Sakarya University Journal of Science , 24 (3) , 494500 . DOI: 10.16984/saufenbilder.627496 
MLA  Mutlu, G , Kır Arpat, E . "Spectral Analysis of Nonselfadjoint Second Order Difference Equation with Operator Coefficient" . Sakarya University Journal of Science 24 (2020 ): 494500 <http://www.saujs.sakarya.edu.tr/en/pub/issue/52472/627496> 
Chicago  Mutlu, G , Kır Arpat, E . "Spectral Analysis of Nonselfadjoint Second Order Difference Equation with Operator Coefficient". Sakarya University Journal of Science 24 (2020 ): 494500 
RIS  TY  JOUR T1  Spectral Analysis of Nonselfadjoint Second Order Difference Equation with Operator Coefficient AU  Gökhan Mutlu , Esra Kır Arpat Y1  2020 PY  2020 N1  doi: 10.16984/saufenbilder.627496 DO  10.16984/saufenbilder.627496 T2  Sakarya University Journal of Science JF  Journal JO  JOR SP  494 EP  500 VL  24 IS  3 SN  2147835X M3  doi: 10.16984/saufenbilder.627496 UR  https://doi.org/10.16984/saufenbilder.627496 Y2  2020 ER  
EndNote  %0 Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi Spectral Analysis of Nonselfadjoint Second Order Difference Equation with Operator Coefficient %A Gökhan Mutlu , Esra Kır Arpat %T Spectral Analysis of Nonselfadjoint Second Order Difference Equation with Operator Coefficient %D 2020 %J Sakarya University Journal of Science %P 2147835X %V 24 %N 3 %R doi: 10.16984/saufenbilder.627496 %U 10.16984/saufenbilder.627496 
ISNAD  Mutlu, Gökhan , Kır Arpat, Esra . "Spectral Analysis of Nonselfadjoint Second Order Difference Equation with Operator Coefficient". Sakarya University Journal of Science 24 / 3 (June 2020): 494500 . https://doi.org/10.16984/saufenbilder.627496 
AMA  Mutlu G , Kır Arpat E . Spectral Analysis of Nonselfadjoint Second Order Difference Equation with Operator Coefficient. SAUJS. 2020; 24(3): 494500. 
Vancouver  Mutlu G , Kır Arpat E . Spectral Analysis of Nonselfadjoint Second Order Difference Equation with Operator Coefficient. Sakarya University Journal of Science. 2020; 24(3): 494500. 
IEEE  G. Mutlu and E. Kır Arpat , "Spectral Analysis of Nonselfadjoint Second Order Difference Equation with Operator Coefficient", Sakarya University Journal of Science, vol. 24, no. 3, pp. 494500, Jun. 2020, doi:10.16984/saufenbilder.627496 