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

页码：2293 / 2320

页数：28

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