Rad HAZU, Matematičke znanosti, Vol. 23 (2019), 85-105.

RESOLVENT OPERATOR OF SINGULAR DIRAC SYSTEM WITH TRANSMISSION CONDITIONS

Bilender P. Allahverdiev and Hüseyin Tuna

Department of Mathematics, Süleyman Demirel University, 32260 Isparta, Turkey
e-mail: bilenderpasaoglu@sdu.edu.tr

Department of Mathematics, Mehmet Akif Ersoy University, 15030 Burdur, Turkey
e-mail: hustuna@gmail.com

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.

2010 Mathematics Subject Classification.   34L40, 34A36, 34A37, 47E05, 34B20, 34L10.

Key words and phrases.   Dirac operator, transmission conditions, singular point, spectral function, Titchmarsh-Weyl function, resolvent operator.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/mnlqgc00ny

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