Failure of analytic hypoellipticity for some operators of \(X^ 2+Y^ 2\) type
type: Item
instance of: scholarly article
title: Failure of analytic hypoellipticity for some operators of \(X^ 2+Y^ 2\) type
zbMATH Open document ID: 0846.35034
author: Toshihiko Hoshiro
published in: Journal of Mathematics of Kyoto University
publication date: 1996-09-29T00:00:00Z
review text: We show that the operator \[ {\partial^2\over \partial x^2}+ \Biggl(x^k {\partial\over \partial y}- x^l {\partial\over \partial t}\Biggr)^2 \] in \(\mathbb{R}^3\) (with nonnegative integers \(k\), \(l\) satisfying \(k< l\)) is not analytically hypoelliptic, if either of the following assumptions is satisfied: (i) \((l+ 1)/(l- k)\) is not a positive integer. (ii) Both \(l-k\) and \((l+ 1)/(l- k)\) are odd integers.
Mathematics Subject Classification ID: 35H10
zbMATH DE Number: 871809
zbMATH Keywords: analytic hypoellipticity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250518648
OpenAlex ID: W1565855909
DOI: 10.1215/KJM/1250518648
description: scientific article; zbMATH DE number 871809