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

Hüseyin Tuna ()
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Hüseyin Tuna: Mehmet Akif Ersoy University

Indian Journal of Pure and Applied Mathematics, 2016, vol. 47, issue 3, 535-544

Abstract: Abstract In this paper we consider a second-order Sturm-Liouville operator of the form $$l(y): = - [p(t)y^\Delta (t)]^\nabla + q(t)y(t)$$ 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.

Keywords: Time scales; Sturm-Liouville operator; Δ-differentiable; dissipative operator; completeness of the system of eigenvectors and associated vectors; Krein theorem; boundary value space (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s13226-016-0196-1

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