scholarly journals On the basis property of the root functions of some class of non-self-adjoint Sturm-Liouville operators

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Cemile Nur ◽  
Oktay A Veliev
Keyword(s):  
Basis Property ◽  
Root Functions ◽  
Sturm Liouville ◽  
Liouville Operators

scholarly journals On Basis Property of Root Functions For a Class Second Order Differential Operator

2020 ◽  
Vol 5 (1) ◽  
pp. 361-368
Author(s):  
Volkan Ala ◽  
Khanlar R. Mamedov
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Equation ◽  
Basis Property ◽  
Second Order ◽  
Order Differential Operator ◽  
Root Functions ◽  
Sturm Liouville

AbstractIn this work we investigate the completeness, minimality and basis properties of the eigenfunctions of one class discontinuous Sturm-Liouville equation with a spectral parameter in boundary conditions.

scholarly journals A 2-edge partial inverse problem for the Sturm-Liouville operators with singular potentials on a star-shaped graph

2018 ◽  
Vol 49 (1) ◽  
pp. 49-66 ◽  
Author(s):  
Natalia Pavlovna Bondarenko
Keyword(s):  
Inverse Problem ◽  
Basis Property ◽  
Singular Potentials ◽  
Main Ingredient ◽  
Riesz Basis Property ◽  
Partial Inverse ◽  
Sturm Liouville ◽  
Shaped Graph ◽  
Partial Inverse Problem ◽  
Liouville Operators

Boundary value problems for Sturm-Liouville operators with potentials from the class $W_2^{-1}$ on a star-shaped graph are considered. We assume that the potentials are known on all the edges of the graph except two, and show that the potentials on the remaining edges can be constructed by fractional parts of two spectra. A uniqueness theorem is proved, and an algorithm for the constructive solution of the partial inverse problem is provided. The main ingredient of the proofs is the Riesz-basis property of specially constructed systems of functions.

scholarly journals Boundary value problems with regular singularities and singular boundary conditions

2005 ◽  
Vol 2005 (9) ◽  
pp. 1481-1495 ◽  
Author(s):  
G. Freiling ◽  
V. Yurko
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Turning Points ◽  
Singular Boundary ◽  
Root Functions ◽  
Sturm Liouville ◽  
System Of Root Functions ◽  
Liouville Operators

Singular boundary conditions are formulated for nonselfadjoint Sturm-Liouville operators with singularities and turning points. For boundary value problems with singular boundary conditions, properties of the spectrum are studied and the completeness of the system of root functions is proved.

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