论文标题
Lie Group $ g =（-1,1）^n $上的全局伪差异操作员
Global pseudo-differential operators on the Lie group $G= (-1,1)^n$
论文作者
论文摘要
在这项工作中，我们表征了hörmander类$ \ symbclasson {m}ρδ{\ group，\ textnormal {hör}} $ on Open歧管$ \ group =（-1,1）^n $。我们表明，通过将开放的流形$ \ group =（-1,1）^n $具有组结构，该组上的相应全局傅立叶分析允许一个人在相位空间$ \ group \ times \ times \ r^n $上定义符号的全局概念。然后，与全局Hörmander类$ \ symbClasson {m}ρδ{\ group \ times \ times \ times \ r^n} $关联的伪分化运算符的类别恢复了Hörmander类$ \ symbClasson {m symbClasson {m}ρδ{\ group，\ textnormal locall locall local plain} $ co。类的分析和定性属性$ \ symbClasson {m}ρδ{\ group \ times \ r^n} $由相应的全局符号表示。特别是，分析了$ l^p $ -fefferman类型的估计和Calderón-Vaillancourt定理，以及操作员的光谱属性。
In this work we characterise the Hörmander classes $\symbClassOn{m}ρδ{\group,\textnormal{Hör}}$ on the open manifold $\group = (-1,1)^n$. We show that by endowing the open manifold $\group = (-1,1)^n$ with a group structure, the corresponding global Fourier analysis on the group allows one to define a global notion of symbol on the phase space $\group \times \R^n$. Then, the class of pseudo-differential operators associated to the global Hörmander classes $\symbClassOn{m}ρδ{\group \times \R^n}$ recovers the Hörmander classes $\symbClassOn{m}ρδ{\group,\textnormal{loc}}$ defined by local coordinate systems. The analytic and qualitative properties of the classes $\symbClassOn{m}ρδ{\group \times \R^n}$ are presented in terms of the corresponding global symbols. In particular, $L^p$-Fefferman type estimates and Calderón-Vaillancourt theorems are analysed, as well as the spectral properties of the operators.
