Spectral analysis of singular Sturm-Liouville operators on time scales

Bilender P. Allahverdiev, Huseyin Tuna

Abstract


In this paper, we consider properties of the spectrum of a Sturm-Liouville
operator on time scales. We will prove that the regular symmetric
Sturm-Liouville operator is semi-bounded from below. We will also give some
conditions for the self-adjoint operator associated with the singular
Sturm-Liouville expression to have a discrete spectrum. Finally, we will
investigate the continuous spectrum of this operator.

Keywords


Sturm-Liouville operator; time scales; splitting method; discrete spectrum; continuous spectrum

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References


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DOI: http://dx.doi.org/10.17951/a.2018.72.1.1-11
Data publikacji: 2018-06-25 09:04:02
Data złożenia artykułu: 2018-06-24 16:20:27

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Copyright (c) 2018 Bilender P. Allahverdiev, Huseyin Tuna