Expansions in Generalized Eigenfunctions of the Weighted Laplacian on Star-shaped Networks

Félix Ali Mehmeti (), Robert Haller-Dintelmann () and Virginie Régnier ()
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Félix Ali Mehmeti: Université de Valenciennes et du Hainaut-Cambrésis Le Mont Houy, Laboratoire de Mathématiques et ses Applications de Valenciennes Institut des Sciences et Techniques de Valenciennes
Robert Haller-Dintelmann: TU Darmstadt, Institut für Mathematik
Virginie Régnier: Université de Valenciennes et du Hainaut-Cambrésis Le Mont Houy, Laboratoire de Mathématiques et ses Applications de Valenciennes Institut des Sciences et Techniques de Valenciennes

A chapter in Functional Analysis and Evolution Equations, 2007, pp 1-16 from Springer

Abstract: Abstract 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.

Keywords: Networks; spectral theory; resolvent; generalized eigenfunctions; functional calculus; evolution equations (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7794-6_1

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DOI: 10.1007/978-3-7643-7794-6_1

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