Dissertation/Thesis Abstract

The discrete Dirac operator and the discrete generalized Weierstrass representation in pseudo-Euclidean spaces
by Zakharov, Dmitry, Ph.D., Columbia University, 2010, 50; 3420881
Abstract (Summary)

In this thesis we consider the problem of finding a integrable discretization of the Dirac operator. We show that an appropriate deformation of the spectral properties of the eigen-function of the smooth Dirac operator leads to a discrete integrable Dirac operator. We use this discrete Dirac operator to construct a discrete analogue of the modified Novikov–Veselov hierarchy and a discrete analogue of the generalized Weierstrass representation of isotropically embedded surfaces in pseudo-Euclidean spaces.

Indexing (document details)
Advisor: Krichever, Igor
School: Columbia University
School Location: United States -- New York
Source: DAI-B 71/09, Dissertation Abstracts International
Subjects: Mathematics, Theoretical Mathematics
Keywords: Dirac operator, Intergrable discretization, Pseudo-Euclidean spaces, Weierstrass representation
Publication Number: 3420881
ISBN: 978-1-124-18579-8
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