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## Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis

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

In this paper, we analyze the non-selfadjoint Sturm-Liouville operator $L$ defined in the Hilbert space $L_{2}(\mathbb{R},H)$ of vector-valued functions which are strongly-measurable and square-integrable in $\mathbb{R}$. $L$ is defined

$L(y)=-y''+Q(x)y,\, x\in\mathbb{R}$

for every $y \in L_{2}(\mathbb{R},H)$ where the potential $Q(x)$ is a non-selfadjoint, completely continuous operator in a separable Hilbert space $H$ for each $x\in \mathbb{R}.$ We obtain the Jost solutions of this operator and examine the analytic and asymptotic properties. Moreover, we find the point spectrum and the spectral singularities of $L$ and also obtain the sufficient condition which assures the finiteness of the eigenvalues and spectral singularities of $L$.

Sturm-Liouville operator equation, eigenvalues, spectral singularities, operator coefficient, non-selfadjoint operators
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-0674-2908Author: Gökhan MUTLU (Primary Author)Institution: Gazı UniversityCountry: Turkey Orcid: 0000-0002-6322-5130Author: Esra KIR ARPAT Institution: Gazı UniversityCountry: Turkey Publication Date : October 6, 2020
 Bibtex @research article { hujms577991, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {1686 - 1694}, doi = {10.15672/hujms.577991}, title = {Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis}, key = {cite}, author = {Mutlu, Gökhan and Kır Arpat, Esra} } APA Mutlu, G , Kır Arpat, E . (2020). Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis . Hacettepe Journal of Mathematics and Statistics , 49 (5) , 1686-1694 . DOI: 10.15672/hujms.577991 MLA Mutlu, G , Kır Arpat, E . "Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis" . Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1686-1694 Chicago Mutlu, G , Kır Arpat, E . "Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 1686-1694 RIS TY - JOUR T1 - Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis AU - Gökhan Mutlu , Esra Kır Arpat Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.577991 DO - 10.15672/hujms.577991 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1686 EP - 1694 VL - 49 IS - 5 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.577991 UR - https://doi.org/10.15672/hujms.577991 Y2 - 2019 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis %A Gökhan Mutlu , Esra Kır Arpat %T Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 5 %R doi: 10.15672/hujms.577991 %U 10.15672/hujms.577991 ISNAD Mutlu, Gökhan , Kır Arpat, Esra . "Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis". Hacettepe Journal of Mathematics and Statistics 49 / 5 (October 2020): 1686-1694 . https://doi.org/10.15672/hujms.577991 AMA Mutlu G , Kır Arpat E . Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1686-1694. Vancouver Mutlu G , Kır Arpat E . Spectral properties of non-selfadjoint Sturm-Liouville operator equation on the real axis. Hacettepe Journal of Mathematics and Statistics. 2020; 49(5): 1686-1694.

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