Asymptotically homogeneous solutions to differential equations with homogeneous polynomial symbols with respect to a multiplicative one-parameter group
type: Item
instance of: scholarly article
title: Asymptotically homogeneous solutions to differential equations with homogeneous polynomial symbols with respect to a multiplicative one-parameter group
zbMATH Open document ID: 1315.46049
DOI: 10.1134/S0081543814040087
author: Yu N. Drozhzhinov
author: B. I. Zav'yalov
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2014-12-17T00:00:00Z
review text: Let \(U = (U_k: k > 0)\) be a multiplicative one-parameter group of linear transformations on \({\mathbb R}^n\) such that all eigenvalues of the generator of the group are positive and let \(P(t)\) be a polynomial such that \(P(U_k t) = t^q P(t)\) for some \(q\in {\mathbb R}.\) Given \(g\in{\mathcal S}^\prime({\mathbb R})\) asymptotically homogeneous at infinity along the group \(U,\) the paper deals with conditions to guarantee that the differential equation \(P(\partial) u = g\) admits a solution which is also asymptotically homogeneous at infinity along the group.
reviewed by: Antonio Galbis
Mathematics Subject Classification ID: 46F99
Mathematics Subject Classification ID: 35R99
zbMATH DE Number: 6381212
zbMATH Keywords: quasiasymptotics
zbMATH Keywords: one-parameter group
zbMATH Keywords: asymptotically homogeneous solution
MaRDI profile type: Publication
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full work available at URL: s0081543814040087
OpenAlex ID: W2079591779
description: scientific article; zbMATH DE number 6381212