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

Bilender PAŞAOĞLU; Hüseyin TUNA

Article Details

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

Authors:

Bilender PAŞAOĞLU | Hüseyin TUNA

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2019 Vol.43 Issue 3, pp.1668-1687

Document Type:

Article

Publication Date:

5/2019

Document Language:

Turkish

Document ID (Org No.):

2000745622

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098

Abstract:

 

We consider the singular Hahn-Dirac system defined by  −1qD−ωq−1,q−1y2+p(x)y1=λy1,−1qD−ωq−1,q−1y2+p(x)y1=λy1,  -\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},D_{\omega,q}y_{1}+r\left(  x\right)  y_{2}  &  =\lambda y_{2},D_{\omega,q}y_{1}+r\left(  x\right)  y_{2}  &  =\lambda y_{2},    where λλ\lambda is a complex spectral parameter and ppp and rrr are real-valued  functions defined on (−∞,∞)(−∞,∞)(-\infty,\infty) and continuous at ω0ω0\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.

Article Details

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

Authors: Bilender PAŞAOĞLU | Hüseyin TUNA

Publisher: TUBITAK

Journal: Turkish Journal of Mathematics 2019 Vol.43 Issue 3, pp.1668-1687

Document Type: Article

Publication Date: 5/2019

Document Language: Turkish

Document ID (Org No.): 2000745622

Frequency: Bimonthly

eISSN: 1303-6149

pISSN: 1300-0098

Issues

Authors:

Bilender PAŞAOĞLU | Hüseyin TUNA

Publisher:

TUBITAK

Journal:

Turkish Journal of Mathematics 2019 Vol.43 Issue 3, pp.1668-1687

Document Type:

Article

Publication Date:

5/2019

Document Language:

Turkish

Document ID (Org No.):

2000745622

Frequency:

Bimonthly

eISSN:

1303-6149

pISSN:

1300-0098