Publisher DOI: 10.1007/978-3-030-44097-8_15
Title: Spectral monotonicity for Schrödinger operators on metric graphs
Language: English
Authors: Rohleder, Jonathan 
Seifert, Christian  
Keywords: Metric graphs; Schrödinger operators; Spectrum; Surgery principles
Issue Date: 2020
Publisher: Birkhäuser
Source: Operator Theory: Advances and Applications (281): 291-310 (2020)
Abstract (english): 
We study the influence of certain geometric perturbations on the spectra of self-adjoint Schrödinger operators on compact metric graphs. Results are obtained for permutation invariant vertex conditions, which, amongst others, include δ and δ′-type conditions. We show that adding edges to the graph or joining vertices changes the eigenvalues monotonically. However, the monotonicity properties may differ from what is known for the previously studied cases of Kirchhoff (or standard) and δ-conditions and may depend on the signs of the coefficients in the vertex conditions.
URI: http://hdl.handle.net/11420/7400
ISSN: 0255-0156
Institute: Mathematik E-10 
Document Type: Chapter (Book)
Part of Series: Operator theory 
Volume number: 281
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