On the absence of the basis property for the root function system of the Sturm–Liouville operator with degenerate boundary conditions

2016 ◽  
Vol 93 (2) ◽  
pp. 220-222 ◽  
Author(s):  
A. S. Makin
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
Root Function ◽  
Basis Property ◽  
Function System ◽  
Sturm Liouville

scholarly journals On Summability of Spectral Expansions Corresponding to the Sturm-Liouville Operator

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Alexander S. Makin
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
Root Function ◽  
Basis Property ◽  
Function System ◽  
Point Boundary ◽  
Spectral Expansions ◽  
Sturm Liouville ◽  
Completeness Property

We study the completeness property and the basis property of the root function system of the Sturm-Liouville operator defined on the segment [0, 1]. All possible types of two-point boundary conditions are considered.

scholarly journals On Stability of Basis Property of Root Vectors System of the Sturm-Liouville Operator with an Integral Perturbation of Conditions in Nonstrongly Regular Samarskii-Ionkin Type Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
N. S. Imanbaev
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
Basis Property ◽  
Differentiation Operator ◽  
Stability And Instability ◽  
Associated Functions ◽  
Sturm Liouville ◽  
Type Boundary ◽  
Eigenfunctions And Associated Functions ◽  
Integral Perturbation

We study a question on stability and instability of basis property of system of eigenfunctions and associated functions of the double differentiation operator with an integral perturbation of Samarskii-Ionkin type boundary conditions.

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