Aspects of Micro-Local Analysis and Geometry in the Study of Lévy-Type Generators

Generators of Feller processes are pseudo-differential operators with negative definite symbols, thus they are objects of micro-local analysis. Continuous negative definite functions (and symbols) give often raise to metrics and these metrics are important to understand, for example, transition functions of certain Feller processes. In this survey we outline some of the more recent results and ideas while at the same time we long to introduce into the field.