Global hypoellipticity for strongly invariant operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Kirilov, Alexandre¹  de Moraes, Wagner A. A.² 

[1] Univ Fed Parana, Dept Matemat, CP 19096, BR-81531990 Curitiba, Parana, Brazil

[2] Univ Fed Parana, Programa Posgrad Matemat, CP 19096, BR-81531990 Curitiba, Parana, Brazil

关键词: Global hypoellipticity;    Invariant operators;    Fourier series;    Subelliptic estimates;    Compact Lie groups;   

DOI  :  10.1016/j.jmaa.2020.123878

来源: Elsevier

【 摘 要 】

In this note, by analyzing the behavior at infinity of the matrix symbol of an invariant operator P with respect to a fixed elliptic operator, we obtain a necessary and sufficient condition to guarantee that P is globally hypoelliptic. As an application, we obtain the characterization of global hypoellipticity on compact Lie groups and examples on the sphere and the torus. We also investigate relations between the global hypoellipticity of P and global subelliptic estimates. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free