$L^2$ boundedness of pseudodifferential operators on manifolds with ends

Shota Fukushima

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arXiv · 2011.06162

$L^2$ boundedness of pseudodifferential operators on manifolds with ends

Shota Fukushima

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Abstract

We investigate properties of pseudodifferential operators on $L^2$ space on manifold with ends including asymptotically conical or hyperbolic ends. Our pseudodifferential operators are a generalization of the canonical quantization which naturally appears in the quantum mechanics on curved spaces. We prove a Calder\'on-Vaillancourt type theorem for our pseudodifferential operators and discuss a construction of parametrix of elliptic differential operators on manifolds with ends.

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Shota Fukushima. 2020-11-12. $L^2$ boundedness of pseudodifferential operators on manifolds with ends. https://arxiv.org/abs/2011.06162

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