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Published in:
2008 | OriginalPaper | Chapter
Expansions in Generalized Eigenfunctions of the Weighted Laplacian on Star-shaped Networks
Authors : Félix Ali Mehmeti, Robert Haller-Dintelmann, Virginie Régnier
Published in: Functional Analysis and Evolution Equations
Publisher: Birkhäuser Basel
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We are interested in evolution phenomena on star-shaped networks composed of
n
semi-infinite branches which are connected at their origins. Using spectral theory we construct the equivalent of the Fourier transform, which diagonalizes the weighted Laplacian on the
n
-star. It is designed for the construction of explicit solution formulas to various evolution equations such as the heat, wave or the Klein-Gordon equation with different leading coefficients on the branches.