GLOBAL HYPOELLIPTICITY, GLOBAL SOLVABILITY AND NORMAL FORM FOR A CLASS OF REAL VECTOR FIELDS ON A TORUS AND APPLICATION

被引：18
|
作者：
Petronilho, G. [1 ]
机构：
[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 363卷 / 12期
基金：
巴西圣保罗研究基金会;
关键词：
Global hypoellipticity; global solvability; normal form; OPERATORS; REGULARITY;
D O I：
10.1090/S0002-9947-2011-05359-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The main purpose of this paper is to present a class of real vector fields defined on a torus for which the concepts of global hypoellipticity and global smooth solvability are equivalent. Furthermore, such a vector field is globally hypoelliptic if and only if its adjoint is globally hypoelliptic, and therefore we can reduce it to its normal form. As an application, we study global C-infinity solvability for certain classes of sub-Laplacians.
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页码：6337 / 6349
页数：13
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