Green Function and Self-adjoint Laplacians on Polyhedral Surfaces
Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1324-1351
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Using Roelcke’s 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.
Kokotov, Alexey; Lagota, Kelvin. Green Function and Self-adjoint Laplacians on Polyhedral Surfaces. Canadian journal of mathematics, Tome 72 (2020) no. 5, pp. 1324-1351. doi: 10.4153/S0008414X19000336
@article{10_4153_S0008414X19000336,
author = {Kokotov, Alexey and Lagota, Kelvin},
title = {Green {Function} and {Self-adjoint} {Laplacians} on {Polyhedral} {Surfaces}},
journal = {Canadian journal of mathematics},
pages = {1324--1351},
year = {2020},
volume = {72},
number = {5},
doi = {10.4153/S0008414X19000336},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000336/}
}
TY - JOUR AU - Kokotov, Alexey AU - Lagota, Kelvin TI - Green Function and Self-adjoint Laplacians on Polyhedral Surfaces JO - Canadian journal of mathematics PY - 2020 SP - 1324 EP - 1351 VL - 72 IS - 5 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000336/ DO - 10.4153/S0008414X19000336 ID - 10_4153_S0008414X19000336 ER -
%0 Journal Article %A Kokotov, Alexey %A Lagota, Kelvin %T Green Function and Self-adjoint Laplacians on Polyhedral Surfaces %J Canadian journal of mathematics %D 2020 %P 1324-1351 %V 72 %N 5 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008414X19000336/ %R 10.4153/S0008414X19000336 %F 10_4153_S0008414X19000336
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