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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 199
The normal symbol on Riemannian manifolds M. Pflaum
On an arbitrary Riemannian manifold $M$ we define the notion of the normal symbol of a pseudo-differential operator $P$ on $M$. This symbol is a certain smooth function on the cotangent bundle $T^*M$ and strongly depends on the Riemannian structure resp. the corresponding connection on $M$. It is shown that modulo smoothing operators resp. symbols we thus receive a linear bijective correspondance between the space of symbols and the space of pseudodifferential operators on $M$.
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