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Dispersive waves with multiple tunnel effect on a star-shaped network

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  • 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 different 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.
    Mathematics Subject Classification: Primary 34B45; Secondary 42A38, 47A10, 47A60, 47A70.


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