Approximation of spectra results for twisted Laplace operators.

Title: Approximation of spectra results for twisted Laplace operators.
Identifier: AAI3283185
identifier: 3283185
Creator: Zahariev, Svetoslav.
Contributor: Adviser: Jozef Dodziuk
Date: 2007
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: To every Hermitian vector bundle with connection over a compact Riemannian manifold M one can associate a corresponding connection Laplacian acting on the sections of the bundle. We define analogous combinatorial metric dependent Laplacians associated to triangulations of M and prove that their spectra converge, as the mesh of the triangulations approaches zero, to the spectrum of the connection Laplacian. We also show how to extend the construction of discrete magnetic Laplace operators on graphs [32] to simplicial complexes.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.