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. 459–491DOI 10.4171/JST/202