Turkish Journal of Mathematics
DOI
10.3906/mat-1902-16
Abstract
We consider the singular Hahn-Dirac system defined by $ -\frac{1}{q}D_{-\omega q^{-1},q^{-1}}y_{2}+p\left( x\right) y_{1} =\lambda y_{1}, $ $D_{\omega,q}y_{1}+r\left( x\right) y_{2} & =\lambda y_{2}, $ where $\lambda$ is a complex spectral parameter and $p$ and $r$ are real-valued functions defined on $(-\infty,\infty)$ and continuous at $\omega_{0}$. 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
First Page
1668
Last Page
1687
Recommended Citation
PAŞAOĞLU, BİLENDER and TUNA, HÜSEYİN
(2019)
"The spectral expansion for the Hahn-Dirac system on the whole line,"
Turkish Journal of Mathematics: Vol. 43:
No.
3, Article 41.
https://doi.org/10.3906/mat-1902-16
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss3/41
