Semi-classical calculus on manifolds with ends and weighted Lp estimates

TL;DR

This paper develops semi-classical pseudo-differential calculus on non-compact manifolds with ends and investigates the boundedness of functions of the semi-classical Laplacian on weighted Lp spaces.

Contribution

It introduces a pseudo-differential expansion framework for functions of the semi-classical Laplacian on manifolds with ends, extending analysis tools to non-compact settings.

Findings

Pseudo-differential expansions for bounded functions of the semi-classical Laplacian.

Weighted Lp boundedness properties of these functions.

Extension of semi-classical analysis to manifolds with ends.

Abstract

For a class of non compact Riemannian manifolds with ends, we give pseudo-differential expansions of bounded functions of the semi-classical Laplacian and study related Lp boundedness properties.