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Spectral properties of the second order difference equation with selfadjoint operator coefficients

Gökhan MUTLU [1]

In this paper, we consider the second order difference equation defined on the whole axis with selfadjoint operator coefficients. The main objective of this study is to obtain the continuous and discrete spectrum of the discrete operator which is generated by this difference equation. To achieve this, we first obtain the Jost solutions of this equation explicitly and then examine the analytical and asymptotic properties of these solutions. With the help of these properties we find the continuous and discrete spectrum of this operator. Finally we obtain the sufficient condition which ensures that this operator has a finite number of eigenvalues.
Difference equations, Jost solution, operator coefficients, continuous spectrum
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Primary Language en Mathematics Research Article Orcid: 0000-0002-0674-2908Author: Gökhan MUTLU (Primary Author)Institution: Gazı UniversityCountry: Turkey Application Date : May 9, 2019 Acceptance Date : August 21, 2019 Publication Date : June 30, 2020
 Bibtex @research article { cfsuasmas562175, journal = {Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, issn = {1303-5991}, eissn = {2618-6470}, address = {Communications Dergi Editörlüğü Ankara Universitesi Fen Fakültesi 06100 Tandoğan ANKARA}, publisher = {Ankara University}, year = {2020}, volume = {69}, pages = {88 - 96}, doi = {10.31801/cfsuasmas.562175}, title = {Spectral properties of the second order difference equation with selfadjoint operator coefficients}, key = {cite}, author = {Mutlu, Gökhan} } APA Mutlu, G . (2020). Spectral properties of the second order difference equation with selfadjoint operator coefficients . Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics , 69 (1) , 88-96 . DOI: 10.31801/cfsuasmas.562175 MLA Mutlu, G . "Spectral properties of the second order difference equation with selfadjoint operator coefficients" . Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 (2020 ): 88-96 Chicago Mutlu, G . "Spectral properties of the second order difference equation with selfadjoint operator coefficients". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 (2020 ): 88-96 RIS TY - JOUR T1 - Spectral properties of the second order difference equation with selfadjoint operator coefficients AU - Gökhan Mutlu Y1 - 2020 PY - 2020 N1 - doi: 10.31801/cfsuasmas.562175 DO - 10.31801/cfsuasmas.562175 T2 - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics JF - Journal JO - JOR SP - 88 EP - 96 VL - 69 IS - 1 SN - 1303-5991-2618-6470 M3 - doi: 10.31801/cfsuasmas.562175 UR - https://doi.org/10.31801/cfsuasmas.562175 Y2 - 2019 ER - EndNote %0 Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Spectral properties of the second order difference equation with selfadjoint operator coefficients %A Gökhan Mutlu %T Spectral properties of the second order difference equation with selfadjoint operator coefficients %D 2020 %J Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics %P 1303-5991-2618-6470 %V 69 %N 1 %R doi: 10.31801/cfsuasmas.562175 %U 10.31801/cfsuasmas.562175 ISNAD Mutlu, Gökhan . "Spectral properties of the second order difference equation with selfadjoint operator coefficients". Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 / 1 (June 2020): 88-96 . https://doi.org/10.31801/cfsuasmas.562175 AMA Mutlu G . Spectral properties of the second order difference equation with selfadjoint operator coefficients. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.. 2020; 69(1): 88-96. Vancouver Mutlu G . Spectral properties of the second order difference equation with selfadjoint operator coefficients. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics. 2020; 69(1): 88-96. IEEE G. Mutlu , "Spectral properties of the second order difference equation with selfadjoint operator coefficients", Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, pp. 88-96, Jun. 2020, doi:10.31801/cfsuasmas.562175

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