Non-self-adjoint singular second-order dynamic operators on time scale


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Allahverdiev B. P.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.42, no.1, pp.229-236, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1002/mma.5338
  • Title of Journal : MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Page Numbers: pp.229-236

Abstract

In this study, maximal dissipative second-order dynamic operators on semi-infinite time scale are studied in the Hilbert space Lr2(T+), that the extensions of a minimal symmetric operator in limit-point case. We construct a self-adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax-Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl-Titchmarsh function of a self-adjoint second-order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators.