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Schrödinger operators on graphs: Symmetrization and Eulerian cycles


Authors: G. Karreskog, P. Kurasov and I. Trygg Kupersmidt
Journal: Proc. Amer. Math. Soc. 144 (2016), 1197-1207
MSC (2010): Primary 34L25, 81U40; Secondary 35P25, 81V99
Published electronically: July 8, 2015
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Abstract: Spectral properties of the Schrödinger operator on a finite compact metric graph with delta-type vertex conditions are discussed. Explicit estimates for the lowest eigenvalue (ground state) are obtained using two different methods: Eulerian cycle and symmetrization techniques.


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Additional Information

G. Karreskog
Affiliation: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden

P. Kurasov
Affiliation: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden

I. Trygg Kupersmidt
Affiliation: Department of Mathematics, Stockholm University, 106 91 Stockholm, Sweden

DOI: https://doi.org/10.1090/proc12784
Keywords: Quantum graphs, ground state
Received by editor(s): February 3, 2015
Received by editor(s) in revised form: March 9, 2015
Published electronically: July 8, 2015
Communicated by: Varghese Mathai
Article copyright: © Copyright 2015 American Mathematical Society