Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity
Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity
复制标题
紧李群和全局亚椭圆性上的伪微分算子 Hörmander 类
DOI：
--
复制
发表时间：
2010
影响因子：
1.2
通讯作者：
J. Wirth
中科院分区：
文献类型：
--
作者：
Michael Ruzhansky;V. Turunen;J. Wirth
本文利用紧李群的表示理论，给出了紧李群上伪微分算子Hörmander类$$Psi ^m(G)$$ Ψm(G)的几个整体刻画。利用这一结果给出了伪微分算子的矩阵值满符号的椭圆性和全局亚椭圆性判据。给出了一阶和二阶全局次椭圆型微分算子的几个例子，特别是局部不可逆但全局不可逆的微分算子。当全局半椭圆性失效时，可以根据全局符号的分析构造显式示例。
In this paper we give several global characterisations of the Hörmander class $$Psi ^m(G)$$Ψm(G) of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.
紧李群上的戈伯格引理、紧致性和算子的基本谱
DOI：
10.1007/s11854-016-0005-0
发表时间：
2016
期刊：
Journal d'Analyse Mathématique
影响因子：
--
作者：
Dasgupta A
通讯作者：
Dasgupta A