On the resolvent of singular Sturm-Liouville operators with transmission conditions


Allahverdiev B. , TUNA H.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.43, no.7, pp.4286-4302, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 7
  • Publication Date: 2020
  • Doi Number: 10.1002/mma.6193
  • Title of Journal : MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Page Numbers: pp.4286-4302
  • Keywords: Hilbert-Schmidt kernel, resolvent operator, singular point, sturm-Liouville problem, spectral function, transmission conditions, Weyl-Titchmarsh function, SPECTRAL THEORY, SCATTERING

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.