On the Bari basis properties of the root functions of non-self adjoint q-Sturm-Liouville problems

2020 ◽  
Keyword(s):  
Root Functions ◽  
Sturm Liouville ◽  
Bari Basis

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 Dissipative eigenvalue problems for a Sturm–Liouville operator with a singular potential

2000 ◽  
Vol 130 (6) ◽  
pp. 1237-1257 ◽  
Author(s):  
Bernhard Bodenstorfer ◽  
Aad Dijksma ◽  
Heinz Langer
Keyword(s):  
Liouville Operator ◽  
Eigenvalue Problems ◽  
Dirichlet Condition ◽  
Continuous Functions ◽  
Dirichlet Boundary Conditions ◽  
Interface Condition ◽  
Associated Functions ◽  
Sturm Liouville ◽  
Bari Basis ◽  
Symmetric Operators

In this paper we consider the Sturm–Liouville operator d2/dx2 − 1/x on the interval [a, b], a < 0 < b, with Dirichlet boundary conditions at a and b, for which x = 0 is a singular point. In the two components L2(a, 0) and L2(0, b) of the space L2(a, b) = L2(a, 0) ⊕ L2(0, b) we define minimal symmetric operators and describe all the maximal dissipative and self-adjoint extensions of their orthogonal sum in L2(a, b) by interface conditions at x = 0. We prove that the maximal dissipative extensions whose domain contains only continuous functions f are characterized by the interface condition limx→0+(f′(x)−f′(−x)) = γf(0) with γ∈C+∪R or by the Dirichlet condition f(0+) = f(0−) = 0. We also show that the corresponding operators can be obtained by norm resolvent approximation from operators where the potential 1/x is replaced by a continuous function, and that their eigen and associated functions can be chosen to form a Bari basis in L2(a, b).

Sign in / Sign up

Export Citation Format

Share Document