The discrete spectrum of Schrödinger operators with -type conditions on regular metric trees

  • Jia Zhao

    Hebei University of Technology, Tianjin, China
  • Guoliang Shi

    Tianjin University, China
  • Jun Yan

    Tianjin University, China
The discrete spectrum of Schrödinger operators with $\delta$-type conditions on regular metric trees cover
Download PDF

A subscription is required to access this article.

Abstract

This paper deals with the spectral properties of the self-adjoint Schrödinger operators with -type conditions on regular metric trees. Firstly, we prove that the operator given in this paper is self-adjoint if it is lower semibounded. Then a necessary and sufficient condition is given for the spectrum of the operator to be discrete. The condition is an analog of Molchanov's discreteness criteria. Finally, using the theory of deficiency indices we get the necessary and sufficient condition which ensures the spectra of the self-adjoint Schrödinger operators with general boundary conditions to be discrete.

Cite this article

Jia Zhao, Guoliang Shi, Jun Yan, The discrete spectrum of Schrödinger operators with -type conditions on regular metric trees. J. Spectr. Theory 8 (2018), no. 2, pp. 459–491

DOI 10.4171/JST/202