Completeness theorem for the dissipative Sturm-Liouville operator on bounded time scales

In this paper we consider a second-order Sturm-Liouville operator of the form l ( y ) := − [ p ( t ) y Δ ( t ) ] ∇ + q ( t ) y ( t ) on bounded time scales. In this study, we construct a space of boundary values of the minimal operator and describe all maximal dissipative, maximal accretive, self-ad...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics 2016-09, Vol.47 (3), p.535-544
Main Author: Tuna, Hüseyin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Boundary conditions
Completeness
Dissipation
Eigenvectors
Mathematics
Mathematics and Statistics
Numerical Analysis
Operators
Sturm-Liouville theory
Theorems
Time
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Summary:In this paper we consider a second-order Sturm-Liouville operator of the form l ( y ) := − [ p ( t ) y Δ ( t ) ] ∇ + q ( t ) y ( t ) on bounded time scales. In this study, we construct a space of boundary values of the minimal operator and describe all maximal dissipative, maximal accretive, self-adjoint and other extensions of the dissipative Sturm-Liouville operators in terms of boundary conditions. Using Krein’s theorem, we proved a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative Sturm-Liouville operators on bounded time scales.
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-016-0196-1