GLOBAL ANALYTIC HYPOELLIPTICITY AND SOLVABILITY OF CERTAIN OPERATORS SUBJECT TO GROUP ACTIONS

被引：3
|
作者：
Araujo, Gabriel [1 ]
Ferra, Igor A. [2 ]
Ragognette, Luis F. [3 ]
机构：
[1] Univ Sao Paulo, ICMC USP, Sao Carlos, SP, Brazil
[2] Univ Fed ABC, CMCC UFABC, Sao Bernardo Do Campo, SP, Brazil
[3] Univ Fed Sao Carlos, DM UFSCar, Sao Carlos, SP, Brazil
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2022年 / 150卷 / 11期
基金：
巴西圣保罗研究基金会;
关键词：
C-INFINITY; REGULARITY;
D O I：
10.1090/proc/16118
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
On T x G, where T is a compact real-analytic manifold and G is a compact Lie group, we consider differential operators P which are invariant by left translations on G and are elliptic in T. Under a mild technical condition, we prove that global hypoellipticity of P implies its global analytic-hypoellipticity (actually Gevrey of any order s >= 1). We also study the connection between the latter property and the notion of global analytic (resp. Gevrey) solvability, but in a much more general setup.
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页码：4771 / 4783
页数：13
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