RESOLVENT OPERATOR OF SINGULAR DIRAC SYSTEM WITH TRANSMISSION CONDITIONS


Allahverdiev B. , Tuna H.

RAD HRVATSKE AKADEMIJE ZNANOSTI I UMJETNOSTI-MATEMATICKE ZNANOSTI, vol.23, no.538, pp.85-105, 2019 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 23 Issue: 538
  • Publication Date: 2019
  • Doi Number: 10.21857/mnlqgc00ny
  • Title of Journal : RAD HRVATSKE AKADEMIJE ZNANOSTI I UMJETNOSTI-MATEMATICKE ZNANOSTI
  • Page Numbers: pp.85-105

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.