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The Parseval Equality and Expansion Formula for Singular Hahn-Dirac System
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Author(s): Bilender P. Allahverdiev (Süleyman Demirel University, Turkey)and Hüseyin Tuna (Mehmet Akif Ersoy University, Turkey)
Copyright: 2020
Pages: 27
Source title:
Emerging Applications of Differential Equations and Game Theory
Source Author(s)/Editor(s): Sırma Zeynep Alparslan Gök (Süleyman Demirel University, Turkey)and Duygu Aruğaslan Çinçin (Süleyman Demirel University, Turkey)
DOI: 10.4018/978-1-7998-0134-4.ch010
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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.
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