FERNANDEZ-BERTOLIN, Aingeru; JAMING, Philippe

doi:10.1007/s10231-019-00896-z

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FERNANDEZ-BERTOLIN, Aingeru
Institut de Mathématiques de Bordeaux [IMB]

JAMING, Philippe
Institut de Mathématiques de Bordeaux [IMB]

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Ce document a été publié dans

Annali di Matematica Pura ed Applicata. 2019

Springer Verlag

Résumé en anglais

We prove that if a solution of the time-dependent Schrödinger equation on an homogeneous tree with bounded potential decays fast at two distinct times then the solution is trivial. For the free Schrödinger operator, we use the spectral theory of the Laplacian and complex analysis and obtain a characterization of the initial conditions that lead to a sharp decay at any time. We then use the recent spectral decomposition of the Schrödinger operator with compactly supported potential due to Colin de Verdièrre and Turc to extend our results in the presence of such potentials. Finally, we use real variable methods first introduced by Escauriaza, Kenig, Ponce and Vega to establish a general sharp result in the case of bounded potentials.< Réduire

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https://oskar-bordeaux.fr/handle/20.500.12278/193254

DOI

http://dx.doi.org/10.1007/s10231-019-00896-z

Project ANR

Initiative d'excellence de l'Université de Bordeaux - ANR-10-IDEX-0003
Analyse Variationnelle en Tomographies photoacoustique, thermoacoustique et ultrasonore - ANR-12-BS01-0001

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Institut de Mathématiques de Bordeaux (IMB) - UMR 5251