scholarly journals On spectral properties of Sturm - Liouville operator with matrix potential

2015 ◽  
Vol 7 (3) ◽  
pp. 84-94 ◽  
Author(s):  
Natal'ya Borisovna Uskova
Keyword(s):  
Liouville Operator ◽  
Spectral Properties ◽  
Matrix Potential ◽  
Sturm Liouville

Spectral Properties of a q-Sturm–Liouville Operator

2008 ◽  
Vol 287 (1) ◽  
pp. 259-274 ◽  
Author(s):  
B. Malcolm Brown ◽  
Jacob S. Christiansen ◽  
Karl Michael Schmidt
Keyword(s):  
Liouville Operator ◽  
Spectral Properties ◽  
Sturm Liouville

scholarly journals Fundamental Spectral Theory of Fractional Singular Sturm-Liouville Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Erdal Bas
Keyword(s):  
Spectral Theory ◽  
Liouville Operator ◽  
Spectral Properties ◽  
Liouville Problem ◽  
Eigenvalues And Eigenfunctions ◽  
Sturm Liouville

We give the theory of spectral properties for eigenvalues and eigenfunctions of Bessel type of fractional singular Sturm-Liouville problem. We show that the eigenvalues and eigenfunctions of the problem are real and orthogonal, respectively. Furthermore, we prove new approximations about the topic.

scholarly journals Spectral properties of an impulsive Sturm–Liouville operator

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Elgiz Bairamov ◽  
Ibrahim Erdal ◽  
Seyhmus Yardimci
Keyword(s):  
Liouville Operator ◽  
Spectral Properties ◽  
Sturm Liouville

scholarly journals Spectral Properties of a Non-Self-Adjoint Differential Operator with Block-Triangular Operator Coefficients

2021 ◽  
Author(s):  
Aleksandr Kholkin
Keyword(s):  
Asymptotic Behavior ◽  
Differential Operator ◽  
Liouville Equation ◽  
Spectral Properties ◽  
Sufficient Conditions ◽  
Triangular Matrix ◽  
Spectral Singularities ◽  
Matrix Potential ◽  
Triangular Operator ◽  
Sturm Liouville

In this chapter, the Sturm-Liouville equation with block-triangular, increasing at infinity operator potential is considered. A fundamental system of solutions is constructed, one of which decreases at infinity, and the second increases. The asymptotic behavior at infinity was found out. The Green’s function and the resolvent for a non-self-adjoint differential operator are constructed. This allows to obtain sufficient conditions under which the spectrum of this non-self-adjoint differential operator is real and discrete. For a non-self-adjoint Sturm-Liouville operator with a triangular matrix potential growing at infinity, an example of operator having spectral singularities is constructed.

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