整体伪微分算子在有边流形上的迹展开与Dixlane可溯性
Expansion of traces and Dixmier traceability for global pseudo-differential operators on manifolds with boundary
摘要：
给定光滑流形$M$（有边界或无边界），本文在非调和分析的背景下研究了整体伪微分学的迹的正则化.事实上，使用[30]中发展的流形（有边界或无边界）上的全局伪微分学、[6]中的Calderón-Vaillancourt定理和全局谓词演算，我们确定了迹正则化中的奇异阶和全局Hörmander类的Dixonian可溯性的尖锐正则阶。我们的分析（免费的坐标系）使我们能够获得非调和模拟的几个经典的结果所产生的正则化的轨迹的微局部分析的伪微分算子与符号定义的本地化。
英文摘要：
Given a smooth manifold $M$ (with or without boundary), in this paper we study the regularisation of traces for the global pseudo-differential calculus in the context of non-harmonic analysis. Indeed, using the global pseudo-differential calculus on manifolds (with or without boundary) developed in [30], the Calderón-Vaillancourt Theorem and the global functional calculus in [6], we determine the singularity orders in the regularisation of traces and the sharp regularity orders for the Dixmier traceability of the global Hörmander classes. Our analysis (free of coordinate systems) allows us to obtain non-harmonic analogues of several classical results arising from the microlocal analysis of regularised traces for pseudo-differential operators with symbols defined by localisations.
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