非紧对称空间上的等变拟微分算子的完全符号
Complete Symbols of Equivariant Pseudodifferential Operators on Noncompact Symmetric Spaces
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中文总结 AI 辅助
该研究针对非紧对称空间G/K上满足快速非对角衰减条件的G-等变Hörmander拟微分算子，定义Harish-Chandra符号函数并刻画其算子类。
中文摘要 AI 辅助
我们研究非紧对称空间G/K上的G-等变Hörmander拟微分算子，对其施瓦茨核满足快速非对角衰减条件的算子，在G的球型缓对偶上定义了称为Harish-Chandra符号函数的完全符号函数概念，并通过该符号函数刻画了此类算子的类。
英文摘要
We study $G$-equivariant Hörmander pseudodifferential operators on a noncompact symmetric space $G/K$. We define a notion of a complete symbol function, called the Harish-Chandra symbol function, on the spherical tempered dual of $G$, for operators that satisfy a rapid off-diagonal decay condition on their Schwartz kernels, and we characterize the class of such operators in terms of their Harish-Chandra symbol function.
