The Parseval Equality and Expansion Formula for Singular Hahn-Dirac System

Author:

Allahverdiev Bilender P.1,Tuna Hüseyin2

Affiliation:

1. Süleyman Demirel University, Turkey

2. Mehmet Akif Ersoy University, Turkey

Abstract

This work studies the singular Hahn-Dirac system given by Here 𝜇 is a complex spectral parameter, p(.) and r(.) are real-valued continuous functions at 𝜔0, defined on [𝜔0,∞) and q∈(0,1), , 𝜔>0, x∈[𝜔0,∞). The existence of a spectral function for this system is proved. Further, a Parseval equality and an expansion formula in eigenfunctions are proved in terms of the spectral function.

Publisher

IGI Global

Reference50 articles.

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4. Allahverdiev B. P. & Tuna H. (2018b). Spectral expansion for the singular Dirac system with impulsive conditions. Turk J Math. 42.2527 – 2545.

5. Allahverdiev B. P. & Tuna H. (2019a). Eigenfunction expansion for singular Sturm-Liouville problems with transmission conditions, Electron. J. Differential Equations, Vol. 2019. No. 03. pp. 1-10.

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