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Green function and self-adjoint Laplacians on polyhedral surfaces

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Green function and self-adjoint Laplacians on polyhedral surfaces

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
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:986137
Deposited By: Kelvin Lagota
Deposited On:25 Jun 2020 17:57
Last Modified:25 Jun 2020 17:57
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