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Pré-Publication, Document De Travail Année : 2016

Topological Resonances on Quantum Graphs

Yves Colin de Verdìère
Francoise Truc

Résumé

In this paper, we try to put the results of Smilansky and al. on "Topological resonances" on a mathematical basis. A key role in the asymptotic of resonances near the real axis for Quantum Graphs is played by the set of metrics for which there exists compactly supported eigenfunctions. We give several estimate of the dimension of this semi-algebraic set, in particular in terms of the girth of the graph. The case of trees is also discussed.
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Dates et versions

hal-01298494 , version 1 (06-04-2016)
hal-01298494 , version 2 (27-02-2018)

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Yves Colin de Verdìère, Francoise Truc. Topological Resonances on Quantum Graphs. 2016. ⟨hal-01298494v1⟩
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