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.
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
