RESOLVENT OPERATOR OF SINGULAR DIRAC SYSTEM WITH TRANSMISSION CONDITIONS
RAD HRVATSKE AKADEMIJE ZNANOSTI I UMJETNOSTI-MATEMATICKE ZNANOSTI, cilt.23, sa.538, ss.85-105, 2019 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 23 Sayı: 538
- Basım Tarihi: 2019
- Doi Numarası: 10.21857/mnlqgc00ny
- Dergi Adı: RAD HRVATSKE AKADEMIJE ZNANOSTI I UMJETNOSTI-MATEMATICKE ZNANOSTI
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.85-105
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
This paper is concerned with the resolvent operator of one dimensional singular Dirac operator with transmission conditions. We study the Titchmarsh-Weyl function of this problem. Later, we construct a Green function and a spectral function for regular and singular problems. With the help of these functions, we obtain an expansion into a Fourier series of resolvent in regular case. Furthermore, we give integral representations in terms of the spectral function for the resolvent of this operator with transmission conditions in singular case. Finally, we obtain a formula for the Titchmarsh-Weyl function in terms of the spectral function of the singular Dirac system.