Basis Properties of the System of Root Functions of the Sturm–Liouville Operator with Degenerate Boundary Conditions: II

2018 ◽  
Vol 54 (12) ◽  
pp. 1566-1582
Author(s):  
A. S. Makin
Keyword(s):  
Boundary Conditions ◽  
Liouville Operator ◽  
Root Functions ◽  
Sturm Liouville ◽  
System Of Root Functions

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 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.

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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