On the relationship between the semiclassical and standard pseudodifferential algebras

Abstract

In this short paper we discuss the precise relationship between the semiclassical and standard pseudodifferential algebras and explore implications such as for large spectral parameter elliptic estimates, even in the case of pseudodifferential spectral familes. We also explain the connection between second microlocalization and this relationship.

12 pages, 1 figure; to appear in Contemporary Mathematics