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- Title
RESOLVENT OPERATOR OF SINGULAR DIRAC SYSTEM WITH TRANSMISSION CONDITIONS.
- Authors
ALLAHVERDIEV, BILENDER P.; TUNA, HÜSEYIN
- Abstract
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.
- Subjects
DIRAC operators; GREEN'S functions; FOURIER series; MATHEMATICAL expansion; DIFFERENTIAL equations
- Publication
Rad HAZU: Matematicke Znanosti, 2019, Vol 23, p85
- ISSN
1845-4100
- Publication type
Article
- DOI
10.21857/mnlqgc00ny