非紧型黎曼对称空间的Oshima紧化上的积分算子。微局部分析与核渐近
Integral operators on the Oshima compactification of a Riemannian symmetric space of non-compact type. Microlocal analysis and kernel asymptotics
摘要：
设$\X\simeq G/K$是非紧型黎曼对称空间，$\widetilde \X$是Oshima紧化，$(π,\mathrm{C}(\widetilde \X))$是$G$在$\widetilde \X$上的正则表示.我们研究了$π(f)$形式的$\widetilde \X$上的积分算子，其中$f$是$G$上的一个快速下降的函数，并在伪微分算子的框架内刻画了它们，描述了它们的核的奇异性.特别地，我们考虑了由强椭圆算子生成的全纯半群与表示$π$，以及它的预解式，并描述了相应的半群和预解式核的渐近行为。
英文摘要：
Let $\X\simeq G/K$ be a Riemannian symmetric space of non-compact type, $\widetilde \X$ its Oshima compactification, and $(π,\mathrm{C}(\widetilde \X))$ the regular representation of $G$ on $\widetilde \X$. We study integral operators on $\widetilde \X$ of the form $π(f)$, where $f$ is a rapidly falling function on $G$, and characterize them within the framework of pseudodifferential operators, describing the singular nature of their kernels. In particular, we consider the holomorphic semigroup generated by a strongly elliptic operator associated to the representation $π$, as well as its resolvent, and describe the asymptotic behavior of the corresponding semigroup and resolvent kernels.
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