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We now show how the ps.d.o. algebra on \(\mathbb {R}^n\) can be transferred to smooth manifolds by using local coordinate charts. The key input is the invariance of the class of m-th order ps.d.o.s under changes of coordinates on \(\mathbb {R}^n\) (Section 5.1). We recall manifolds and differential operators on them in Sections 5.2–5.3. We define ps.d.o.s on manifolds and discuss their algebra and symbolic properties in Sections 5.4–5.8; we explain this passage to manifolds in considerable detail.

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Pseudodifferential Operators on Manifolds

  • 章节

  • 发表日期：

    2025年

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  • Peter Hintz

摘要

We now show how the ps.d.o. algebra on \(\mathbb {R}^n\) can be transferred to smooth manifolds by using local coordinate charts. The key input is the invariance of the class of m-th order ps.d.o.s under changes of coordinates on \(\mathbb {R}^n\) (Section 5.1). We recall manifolds and differential operators on them in Sections 5.2–5.3. We define ps.d.o.s on manifolds and discuss their algebra and symbolic properties in Sections 5.4–5.8; we explain this passage to manifolds in considerable detail.