scholarly journals On Basis Property of Root Functions for a Class of the Second Order Differential Operators

2020 ◽  
Vol 12 (3) ◽  
pp. 15-21
Author(s):  
V. Ala ◽  
◽  
Kh.R. Mamedov ◽  
Keyword(s):  
Differential Operators ◽  
Basis Property ◽  
Second Order ◽  
Root Functions

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 Equiconvergence property for spectral expansions related to perturbations of the operator - u''(-x) with initial data

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1069-1078 ◽  
Author(s):  
Leonid Kritskov ◽  
Abdizhahan Sarsenbi
Keyword(s):  
Spectral Analysis ◽  
Initial Data ◽  
Differential Operators ◽  
Second Order ◽  
Spectral Expansions ◽  
Root Functions ◽  
Operator Form ◽  
Complex Valued

Uniform equiconvergence of spectral expansions related to the second-order differential operators with involution: -u''(-x) and -u''(-x) + q(x)u(x) with the initial data u(-1) = 0, u'(-1) = 0 is obtained. Starting with the spectral analysis of the unperturbed operator, the estimates of the Green?s functions are established and then applied via the contour integrating approach to the spectral expansions. As a corollary, it is proved that the root functions of the perturbed operator form the basis in L2(-1,1) for any complex-valued coefficient q(x) ? L2(-1,1).

Sign in / Sign up

Export Citation Format

Share Document