A criterion for hypoellipticity of operators constructed from vector fields
A criterion for hypoellipticity of operators constructed from vector fields
复制标题
DOI：
10.1080/03605307908820107
复制
发表时间：
1979
影响因子：
1.9
通讯作者：
L. Rothschild
中科院分区：
文献类型：
--
作者：
L. Rothschild
0.导论.假设X1，X2，.，是流形M上光滑的真实的向量场。设L是微分算子，其中xa= XX. x a=（alta2，...，a1，”1 a2”Pp la（= p）和aa（x）是光滑的复值函数。我们寻求最少的限制性条件，将保证L是hypoelliptical，即如果Lf= g与g光滑在一个开放集U r然后f也是光滑的U。版权O 1979年由马塞尔Dekker公司。All Rights Reserved.未经出版商书面许可，不得以任何形式或任何方式（电子或机械）复制或传播本作品或其任何部分，包括影印、缩微拍摄和记录，或通过任何信息存储和检索系统。
0. Introduction. Suppose that X1, X 2,..., X P are smooth, real vector fields on a manifold M. Let L be the differential operator where xa= XX... x a=(alta2,..., a 1," 1 a2" Pp la (= p and the aa (x) are smooth, complex-valued functions. We seek the least restrictive conditions that will guarantee that L is hypoelliptic, ie that if Lf= g with g smooth in an open set U r then f is also smooth in U.Copyright O 1979 by Marcel Dekker, Inc. All Rights Reserved. Neither this work nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher.