arXiv Analytics

Sign in

arXiv:1902.03232 [math.SP]AbstractReferencesReviewsResources

Green function and self-adjoint Laplacians on polyhedral surfaces

Alexey Kokotov, Kelvin Lagota

Published 2019-02-08Version 1

Using Roelcke formula for the Green function, we explicitly construct a basis in the kernel of the adjoint Laplacian on a compact polyhedral surface $X$ and compute the $S$-matrix of $X$ at the zero value of the spectral parameter. We apply these results to study various self-adjoint extensions of a symmetric Laplacian on a compact polyhedral surface of genus two with a single conical point. It turns out that the behaviour of the $S$-matrix at the zero value of the spectral parameter is sensitive to the geometry of the polyhedron.

Related articles: Most relevant | Search more
arXiv:1505.07606 [math.SP] (Published 2015-05-28)
Green Operators of Networks with a new vertex
arXiv:0803.0566 [math.SP] (Published 2008-03-04)
Inverse eigenvalue problems for Sturm-Liouville equations with spectral parameter linearly contained in one of the boundary conditions
arXiv:math/9810044 [math.SP] (Published 1998-10-07)
Removal of the resolvent-like dependence on the spectral parameter from perturbations