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Absolutely Continuous Spectrum for Laplacians on Radial Metric Trees and Periodicity
Publikationstyp
Journal Article
Date Issued
2017-11-01
Sprache
English
Author(s)
Institut
TORE-URI
Volume
89
Issue
3
Start Page
439
End Page
453
Citation
Integral Equations and Operator Theory 3 (89): 439-453 (2017-11-01)
Publisher DOI
Scopus ID
On an infinite, radial metric tree graph we consider the corresponding Laplacian equipped with self-adjoint vertex conditions from a large class including δ- and weighted δ′-couplings. Assuming the numbers of different edge lengths, branching numbers and different coupling conditions to be finite, we prove that the presence of absolutely continuous spectrum implies that the sequence of geometric data of the tree as well as the coupling conditions are eventually periodic. On the other hand, we provide examples of self-adjoint, non-periodic couplings which admit absolutely continuous spectrum.
Subjects
Absolutely continuous spectrum
Quantum graph
Schrödinger operator
Tree