On the divergence of expansions in systems of root functions of the Sturm-Liouville operator with degenerate boundary conditions

2012 ◽  
Vol 48 (8) ◽  
pp. 1183-1187 ◽  
Author(s):  
A. S. Makin
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
Root Functions ◽  
Sturm Liouville

scholarly journals On the Riesz Basisness of Systems Composed of Root Functions of Periodic Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Alp Arslan Kıraç
Keyword(s):  
Boundary Conditions ◽  
Riesz Basis ◽  
Liouville Operator ◽  
Periodic Boundary ◽  
Fourier Coefficients ◽  
Sufficient Conditions ◽  
Root Functions ◽  
Periodic Boundary Value Problems ◽  
Sturm Liouville ◽  
Necessary And Sufficient

We consider the nonself-adjoint Sturm-Liouville operator withq∈L1[0,1]and either periodic or antiperiodic boundary conditions. We obtain necessary and sufficient conditions for systems of root functions of these operators to be a Riesz basis inL2[0,1]in terms of the Fourier coefficients ofq.

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.

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.

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