Lagota, Kelvin (2019) Green function and self-adjoint Laplacians on polyhedral surfaces. PhD thesis, Concordia University.
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Abstract
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.
Divisions: | Concordia University > Faculty of Arts and Science > Mathematics and Statistics |
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Item Type: | Thesis (PhD) |
Authors: | Lagota, Kelvin |
Institution: | Concordia University |
Degree Name: | Ph. D. |
Program: | Mathematics |
Date: | 23 September 2019 |
Thesis Supervisor(s): | Kokotov, Alexey and Kalvin, Victor |
ID Code: | 987181 |
Deposited By: | Kelvin Lagota |
Deposited On: | 29 Jun 2021 23:28 |
Last Modified: | 29 Jun 2021 23:28 |
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