Authors: BİLENDER PAŞAOĞLU, HÜSEYİN TUNA
Abstract: We consider the singular Hahn-Dirac system defined by −1qD−ωq−1,q−1y2+p(x)y1=λy1, D_{\omega,q}y_{1}+r\left( x\right) y_{2} & =\lambda y_{2}, where λ is a complex spectral parameter and p and r are real-valued functions defined on (−∞,∞) and continuous at ω0. We prove the existence of a spectral function for such a system. We also prove the Parseval equality and the spectral expansion formula in terms of the spectral function for this system on the whole line.
Keywords: Hahn-Dirac system, singular point, Parseval equality, spectral function, spectral expansion
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