On strongly hypoelliptic polynomials
type: Item
instance of: scholarly article
title: On strongly hypoelliptic polynomials
zbMATH Open document ID: 0896.35033
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 1998-03-24T00:00:00Z
review text: The author studies strongly hypoelliptic polynomials. A multivariate polynomial \(P\) is strongly hypoelliptic if \(P(\xi)\rightarrow\infty\) as \(\| \xi\| \rightarrow\infty\) and there exist constants \(c,M>0\) such that \(| P(\xi)| \leq cd_P^m(\xi)\), \(\xi\in\mathbb R^n\), \(\| \xi\| \geq M\), \(m=\text{ord}(P)\equiv \max_{\alpha\in(P)}| \alpha| \), where \(d_P(\xi)\) is the distance from the point \(\xi\) to the set \({\mathcal D}(P)=\{\theta\in\mathbb C^n\); \(P(\theta)=0\}\). In the main result there are described sufficient and necessary conditions for a polynomial to be strongly hypoelliptic. The conditions are obtained from the study of linear transformations of strongly hypoelliptic polynomials and of the growth and strong hypoellipticity.
reviewed by: Doru Ştefănescu
Mathematics Subject Classification ID: 35H10
Mathematics Subject Classification ID: 12D99
zbMATH DE Number: 1131848
zbMATH Keywords: sufficient and necessary conditions
author: Vachagan N. Margaryan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1131848