A basis for polynomial solutions to systems of linear constant coefficient PDE's
type: Item
instance of: scholarly article
title: A basis for polynomial solutions to systems of linear constant coefficient PDE's
zbMATH Open document ID: 0849.35080
author: Paul S. Pedersen
published in: Advances in Mathematics
publication date: 1996-05-19T00:00:00Z
review text: Let \(P_k(x)\), \(k= 1, 2,\dots, m\), be polynomials in \(n\) variables with coefficients from \(K\) (\(K= \mathbb{C}\) or \(K= \mathbb{N}\)) and let \(N_{\leq M}\) be the set of all polynomial solutions of degree not greater than \(M\) to the system of partial differential equations: \(P_k(D) u(x)= 0\), \(k= 1, 2,\dots, m\) (\(m\) equations and only one unknown function). To study the set \(N_{\leq M}\) a certain associative and commutative algebra defined over \(K\) is introduced. The method of finding an easily computed (as the author claims) basis for the vector space \(N_{\leq M}\) is given. There are three illustrate examples.
Mathematics Subject Classification ID: 35N05
Mathematics Subject Classification ID: 35E20
zbMATH DE Number: 859776
zbMATH Keywords: basis for polynomial solutions
reviewed by: Valery V. Karachik
MaRDI profile type: Publication
full work available at URL: aima.1996.0005
OpenAlex ID: W2060759847
DOI: 10.1006/AIMA.1996.0005
description: scientific article; zbMATH DE number 859776