Globally hypoelliptic triangularizable systems of periodic pseudo-differential operators

被引：1
|
作者：
Silva, Fernando de Avila [1 ,2 ]
机构：
[1] Univ Fed Parana, Dept Matemat, Curitiba, Parana, Brazil
[2] Caixa Postal 19081, BR-81531990 Curitiba, Brazil
来源：
MATHEMATISCHE NACHRICHTEN | 2023年 / 296卷 / 06期
关键词：
Fourier series; global hypoellipticity; pseudo-differential operators; triangularization; VECTOR-FIELDS; HYPERBOLIC SYSTEMS; SOLVABILITY; TORUS;
D O I：
10.1002/mana.202100132
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper presents an investigation on the global hypoellipticity problem for a class of systems of pseudo-differential operators on the torus. The approach consists in establishing conditions on the matrix symbol of the system such that it can be transformed into a suitable triangular form involving a nilpotent upper triangular matrix. Hence, the global hypoellipticity is studied by analyzing the behavior of the eigenvalues and their averages.
引用
收藏
页码：2293 / 2320
页数：28
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