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Spectral monotonicity for Schrödinger operators on metric graphs
Publikationstyp
Book Part
Date Issued
2020
Sprache
English
Author(s)
Institut
TORE-URI
First published in
Number in series
281
Start Page
291
End Page
310
Citation
Operator Theory: Advances and Applications (281): 291-310 (2020)
Publisher DOI
Scopus ID
Publisher
Birkhäuser
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.
Subjects
Metric graphs
Schrödinger operators
Spectrum
Surgery principles