On Expansion in Eigenfunction for Dirac Systems on the Unbounded Time Scales


PAŞAOĞLU B., TUNA H.

Differential Equations and Dynamical Systems, vol.30, pp.271-285, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30
  • Publication Date: 2022
  • Doi Number: 10.1007/s12591-019-00488-6
  • Journal Name: Differential Equations and Dynamical Systems
  • Journal Indexes: Emerging Sources Citation Index, Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.271-285
  • Keywords: Time scales, Dirac operator, Singular point, Spectral function, Parseval equality, Eigenfunction expansion, BOUNDARY-VALUE-PROBLEMS

Abstract

In this work, we consider one dimensional Dirac operators on unbounded time scales. We construct a spectral function of such an operator. Using this function, we establish a Parseval equality and an expansion formula in eigenfunctions for the Dirac operator on unbounded time scales.