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Discreteness of spectrum for Schrödinger operators with δʹ-type conditions on infinite regular trees

Part of: General theory of linear operators Ordinary differential operators Boundary value problems

Published online by Cambridge University Press:  14 August 2017

Jia Zhao ,
Guoliang Shi  and
Jun Yan
Jia Zhao
Affiliation:
Department of Mathematics, School of Science, Hebei University of Technology, Tianjin 300401, People's Republic of China (zhaojia@hebut.edu.cn)
Guoliang Shi
Affiliation:
School of Mathematics, Tianjin University, Tianjin 300354, People's Republic of China (glshi@tju.edu.cn; , jun.yan@tju.edu.cn)
Jun Yan
Affiliation:
School of Mathematics, Tianjin University, Tianjin 300354, People's Republic of China (glshi@tju.edu.cn; , jun.yan@tju.edu.cn)
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Extract

This paper deals with the spectral properties of self-adjoint Schrödinger operators with δʹ-type conditions on infinite regular trees. Firstly, we discuss the semi-boundedness and self-adjointness of this kind of Schrödinger operator. Secondly, by using the form approach, we give the necessary and sufficient condition that ensures that the spectra of the self-adjoint Schrödinger operators with δʹ-type conditions are discrete.

Keywords

regular metric treeSchrödinger operatorδʹ-type conditionsdiscrete spectrum

MSC classification

Secondary: 34B45: Boundary value problems on graphs and networks 34L05: General spectral theory 47A10: Spectrum, resolvent 47A25: Spectral sets
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 5 , October 2017 , pp. 1091 - 1117
Copyright
Copyright © Royal Society of Edinburgh 2017 

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