Processing math: 100%

The spectral expansion for the Hahn-Dirac system on the whole line

Authors: BİLENDER PAŞAOĞLU, HÜSEYİN TUNA

Abstract: We consider the singular Hahn-Dirac system defined by 1qDωq1,q1y2+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

Full Text: PDF