Spectral Theory of Singular Hahn Difference Equation of the Sturm-Liouville Type

Allahverdiev, Bilender P.; Tuna, Hüseyin

doi:10.2478/cm-2020-0002

Cited by 5 publications

(3 citation statements)

References 31 publications

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“…Historically, in 1910, H. Weyl was …rst obtained a representation theorem for the resolvent of Sturm-Liouville problem de…ned by (py 0 ) 0 + qy = y; x 2 (0; 1); where p; q are real-valued and p 1 ; q 2 L 1 loc [0; 1). Similar representation theorems were proved in [25,20,2,5,6,7].…”

Section: Introductionsupporting

confidence: 73%

On the resolvent of singular q-Sturm-Liouville operators

Paşaoğlu¹,

Tuna²

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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In this paper, we investigate the resolvent operator of the singular q-Sturm-Liouville problem de…ned aswith the boundary conditionwhere 2 C, r is a real-valued function de…ned on [0; 1), continuous at zero and r 2 L 1 q;loc [0; 1). We give a representation for the resolvent operator and investigate some properties of this operator. Furthermore, we obtain a formula for the Titchmarsh-Weyl function of the singular q-Sturm-Liouville problem.

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Section: Introductionsupporting

confidence: 73%

On the resolvent of singular q-Sturm-Liouville operators

Paşaoğlu¹,

Tuna²

2021

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…One can prove that z and D ω,q z are continuous at ω 0 . It is obvious that the function Z satisfies (3).…”

Section: Definition 3 ([6]mentioning

confidence: 99%

On extensions of matrix-valued Hahn–Sturm–Liouville operators

Allahverdiev¹,

Tuna²

2022

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In this paper, we study matrix-valued Hahn-Sturm-Liouville equations. We give an existence and uniqueness result. We introduce the corresponding maximal and minimal operators for this system, and some properties of these operators are investigated. Finally, we characterize extensions (maximal dissipative, maximal accumulative and self-adjoint) of the minimal symmetric operator. Introduction.As is known, extension theory of symmetric operators is one of the main research areas of operator theory. This theory was studied earlier [33]. In [17], the description of self-adjoint extensions of a symmetric operator was given. obtained extensions of a symmetric operator with aid of linear relations. Later, in [16,24], the notion of a space of boundary values was introduced. In [26], a description of extensions of a second-order symmetric operator was given. In [19], the author obtained a description of self-adjoint extensions of Sturm-Liouville operators with an operator potential. In the case when the deficiency indices take indeterminate values, a description of extensions of differential operators was given in [1,[28][29][30]. The readers may find some papers related to extension theory in [20,24,35].Matrix-valued Sturm-Liouville equations arise in a variety of physical problems (for example, see [5, 10-15, 18, 34]). While there are several results

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“…They defined a Hilbert space of

q,\omega

square summable functions and gave the properties of the eigenvalues and the eigenfunctions. The spectral theory of singular Hahn difference equation of the Sturm–Liouville type was studied by Allahverdiev and Tuna [24].…”

Section: Introductionmentioning

confidence: 99%