A reproducing kernel function and convergence properties for discrete analytic functions
Bolen, James Cordell
Bolen, James Cordell
Citations
Altmetric:
Soloist
Composer
Publisher
Date
1968
Additional date(s)
Abstract
In 1944, J. Ferrand introduced the concept of a discrete analytic function. Many properties of discrete analytic functions were developed by R. J. Duffin in 1956. In the first part of this dissertation a reproducing kernel is defined and is shown to have analogous properties of the Bergman kernel for analytic functions. The next part of the paper discusses various types of convergence of discrete analytic functions to a given analytic function defined on a simply connected domain, Finally, it is shown that it is not reasonable to expect the discrete kernels to converge to the Bergman kernel defined on a simply connected domain.
Contents
Subject
Subject(s)
Analytic functions
Kernel functions
Convergence
Kernel functions
Convergence
Research Projects
Organizational Units
Journal Issue
Genre
Dissertation
Description
Format
iii, 54 leaves, bound
Department
Mathematics