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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series S Année : 2013

Dispersive waves with multiple tunnel effect on star shaped networks

Résumé

We consider the Klein-Gordon equation on a star-shaped network composed of n half-axes connected at their origins. We add a potential which is constant but dierent on each branch. The corresponding spatial operator is self-adjoint and we state explicit expressions for its resolvent and its resolution of the identity in terms of generalized eigenfunctions. This leads to a generalized Fourier type inversion formula in terms of an expansion in generalized eigenfunctions. This paper is a survey of a longer article, nevertheless the proof of the central formula is indicated.
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Dates et versions

hal-03227666 , version 1 (17-05-2021)

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Felix Ali Mehmeti, Robert Haller-Dintelmann, Virginie Régnier. Dispersive waves with multiple tunnel effect on star shaped networks. Discrete and Continuous Dynamical Systems - Series S, 2013, 6 (3), pp.783-791. ⟨10.3934/dcdss.2013.6.783⟩. ⟨hal-03227666⟩
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