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

Subjects 
Mathematics

Journal Section 
Research Article 
Authors 
Orcid: 0000000206742908 Author: Gökhan MUTLU (Primary Author) Institution: Gazı University Country: Turkey

Dates 
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 = {13035991},
eissn = {26186470},
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) ,
8896 .
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
): 8896 <https://dergipark.org.tr/en/pub/cfsuasmas/issue/49221/562175>

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
): 8896 
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  1303599126186470
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 1303599126186470
%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):
8896
. 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):
8896.

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):
8896.

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.
8896, Jun. 2020, doi:10.31801/cfsuasmas.562175
