Existence of a spectral measure for second-order delta dynamic equations on semi-infinite time scale intervals

Adil Huseynov

Chaos, Solitons & Fractals, 2011, vol. 44, issue 9, 769-777

Abstract: In this study, we prove existence of a spectral measure (or orthogonality measure) for second-order delta dynamic equations on semi-infinite time scale intervals. A Parseval equality and an expansion in eigenfunctions formula are established in terms of the spectral measure. The result obtained unifies the well-known results on existence of a spectral measure for Sturm–Liouville operators on the real semi-axis and for semi-infinite Jacobi matrices, and extends them to variety of numerous time scales which may, in particular, be fractals.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:44:y:2011:i:9:p:769-777

DOI: 10.1016/j.chaos.2011.07.002

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