Abstract
We consider the Klein-Gordon equation on a star-shaped networkcomposed of $n$ half-axes connected at their origins. We add apotential which is constant but different on each branch. Thecorresponding spatial operator is self-adjoint and we state explicitexpressions for its resolvent and its resolution of the identity interms of generalized eigenfunctions. This leads to a generalizedFourier type inversion formula in terms of an expansion ingeneralized eigenfunctions. This paper is a survey of a longerarticle, nevertheless the proof of the central formula is indicated.
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