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

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 Calderón-Vaillancourt type theorem for our pseudodifferential operators and discuss a construction of parametrix of elliptic differential operators on manifolds with ends.

arXiv comment29 pages

References in corpus (1)

• Pseudodifferential Weyl Calculus on (Pseudo-)Riemannian Manifolds