Boundary value problems for partial difference equations
type: Item
instance of: scholarly article
title: Boundary value problems for partial difference equations
zbMATH Open document ID: 0862.39002
DOI: 10.1007/BF01827809
author: Jan Veit
published in: Multidimensional Systems and Signal Processing
publication date: 1997-05-25T00:00:00Z
review text: The paper deals with linear partial difference equations of the form \[ \sum_{p\in B}b(p,l)y(l-p)= x(l),\quad l\in A\subseteq\mathbb{Z}^d, \] where \(\mathbb{Z}^d\) is the set of \(d\)-dimensional vectors with integer coordinates, \(A\) is an arbitrary non-empty subset of \(\mathbb{Z}^d\) and \(B\) is a finite subset of \(\mathbb{Z}^d\) containing the zero vector as well as at least one non-zero vector. The functions \(b(p,l)\) and \(x(l)\) are complex-valued. For certain boundary value problems conditions are formulated ensuring the uniqueness of solutions. Using the concept of fundamental solutions also results on the existence and construction of solutions are proved. Various examples illustrate the results of this paper.
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 890723
zbMATH Keywords: linear partial difference equations
zbMATH Keywords: boundary value problems
zbMATH Keywords: fundamental solutions
reviewed by: Bernd Aulbach
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 890723