Mathematics – Spectral Theory
Scientific paper
2009-06-17
Mathematics
Spectral Theory
24 pages, 1 figure
Scientific paper
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. The characteristics of the problem are marked by the non-manifold character of the star-shaped domain. Therefore the approach via the Sturm-Liouville theory for systems is not well-suited.
Haller-Dintelmann Robert
Mehmeti Felix Ali
Régnier Virginie
No associations
LandOfFree
The Klein-Gordon equation with multiple tunnel effect on a star-shaped network: Expansions in generalized eigenfunctions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Klein-Gordon equation with multiple tunnel effect on a star-shaped network: Expansions in generalized eigenfunctions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Klein-Gordon equation with multiple tunnel effect on a star-shaped network: Expansions in generalized eigenfunctions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-223591