GLOBAL PROPERTIES OF VECTOR FIELDS ON COMPACT LIE GROUPS IN KOMATSU CLASSES. II. NORMAL FORMS

被引:1
作者
Kirilov, Alexandre [1 ]
de Moraes, Wagner A. A. [1 ]
Ruzhansky, Michael [2 ,3 ]
机构
[1] Univ Fed Parana, Dept Matemat, CP 19096, BR-81531990 Curitiba, PR, Brazil
[2] Univ Ghent, Dept Math Anal Log & Discrete Math, B-9000 Ghent, Belgium
[3] Queen Mary Univ London, Sch Math Sci, London, England
基金
英国工程与自然科学研究理事会;
关键词
compact Lie groups; global hypoellipticity; global solvability; Komatsu classes; normal form; ULTRADIFFERENTIABLE FUNCTIONS; HYPOELLIPTICITY; SOLVABILITY; ULTRADISTRIBUTIONS; TORUS;
D O I
10.3934/cpaa.2022128
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Let G(1) and G(2) be compact Lie groups, X-1 is an element of g(1), X-2 is an element of g(2) and consider the operator Laq = X-1 + a(x(1))X-2 + q(x(1), x(2)), where a and q are ultradifferentiable functions in the sense of Komatsu, and a is real-valued. Assuming certain condition on a and q we characterize completely the global hypoellipticity and the global solvability of Laq in the sense of Komatsu. For this, we present a conjugation between Laq and a constant-coefficient operator that preserves these global properties in Komatsu classes. We also present examples of globally hypoelliptic and globally solvable operators on T(1 )x S-3 and S-3 x S(3 )in the sense of Komatsu. In particular, we give examples of differential operators which are not globally C-infinity-solvable, but are globally solvable in Gevrey spaces.
引用
收藏
页码:3919 / 3940
页数:22
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