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## Spectral Analysis of Non-selfadjoint Second Order Difference Equation with Operator Coefficient

#### Gökhan MUTLU [1] , Esra KIR ARPAT [2]

In this paper, we consider the discrete Sturm-Liouville operator generated by second order difference equation with non-selfadjoint operator coefficient. This operator is the discrete analogue of the Sturm-Liouville differential operator generated by Sturm-Liouville 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.

Sturm-Liouville’s operator equation, Non-selfadjoint operators, Discrete operators, Continuous spectrum, Operator coefficients
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Primary Language en Mathematics June-2020 Research Articles Orcid: 0000-0002-0674-2908Author: Gökhan MUTLU (Primary Author)Institution: Gazı UniversityCountry: Turkey Orcid: 0000-0002-6322-5130Author: Esra KIR ARPATInstitution: Gazı University Application Date : October 1, 2019 Acceptance Date : March 20, 2020 Publication Date : June 1, 2020
 Bibtex @research article { saufenbilder627496, journal = {Sakarya University Journal of Science}, issn = {}, eissn = {2147-835X}, address = {}, publisher = {Sakarya University}, year = {2020}, volume = {24}, pages = {494 - 500}, doi = {10.16984/saufenbilder.627496}, title = {Spectral Analysis of Non-selfadjoint 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 Non-selfadjoint Second Order Difference Equation with Operator Coefficient . Sakarya University Journal of Science , 24 (3) , 494-500 . DOI: 10.16984/saufenbilder.627496 MLA Mutlu, G , Kır Arpat, E . "Spectral Analysis of Non-selfadjoint Second Order Difference Equation with Operator Coefficient" . Sakarya University Journal of Science 24 (2020 ): 494-500 Chicago Mutlu, G , Kır Arpat, E . "Spectral Analysis of Non-selfadjoint Second Order Difference Equation with Operator Coefficient". Sakarya University Journal of Science 24 (2020 ): 494-500 RIS TY - JOUR T1 - Spectral Analysis of Non-selfadjoint 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 - -2147-835X 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 Non-selfadjoint Second Order Difference Equation with Operator Coefficient %A Gökhan Mutlu , Esra Kır Arpat %T Spectral Analysis of Non-selfadjoint Second Order Difference Equation with Operator Coefficient %D 2020 %J Sakarya University Journal of Science %P -2147-835X %V 24 %N 3 %R doi: 10.16984/saufenbilder.627496 %U 10.16984/saufenbilder.627496 ISNAD Mutlu, Gökhan , Kır Arpat, Esra . "Spectral Analysis of Non-selfadjoint Second Order Difference Equation with Operator Coefficient". Sakarya University Journal of Science 24 / 3 (June 2020): 494-500 . https://doi.org/10.16984/saufenbilder.627496 AMA Mutlu G , Kır Arpat E . Spectral Analysis of Non-selfadjoint Second Order Difference Equation with Operator Coefficient. SAUJS. 2020; 24(3): 494-500. Vancouver Mutlu G , Kır Arpat E . Spectral Analysis of Non-selfadjoint Second Order Difference Equation with Operator Coefficient. Sakarya University Journal of Science. 2020; 24(3): 494-500. IEEE G. Mutlu and E. Kır Arpat , "Spectral Analysis of Non-selfadjoint Second Order Difference Equation with Operator Coefficient", Sakarya University Journal of Science, vol. 24, no. 3, pp. 494-500, Jun. 2020, doi:10.16984/saufenbilder.627496

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