On the resolvent of singular Sturm-Liouville operators with transmission conditions |
| |
| Authors: | Bilender P. Allahverdiev Hüseyin Tuna |
| |
| Affiliation: | 1. Department of Mathematics, Süleyman Demirel University, Isparta, 32260 Turkey;2. Department of Mathematics, Mehmet Akif Ersoy University, Burdur, 15030 Turkey |
| |
| Abstract: | In this article, we investigate the resolvent operator of singular Sturm-Liouville problem with transmission conditions. We obtain integral representations for the resolvent of this operator in terms of the spectral function. Later, we discuss some properties of the resolvent operator, such as Hilbert-Schmidt kernel property, compactness. Finally, we give a formula in terms of the spectral function for the Weyl-Titchmarsh function of this problem. |
| |
| Keywords: | Hilbert-Schmidt kernel resolvent operator singular point sturm-Liouville problem spectral function transmission conditions Weyl-Titchmarsh function |
|
|
