Analysis Seminar: "Sobolev algebras on Lie groups"

Abstract: The question of when a Sobolev space is an algebra has a long history. In this talk, we first review the classical problem and its variation in R^n (due to Strichartz) and on a nilpotent Lie group.  We also discuss the possible definitions of Sobolev spaces in more general settings, such as a manifold or a Lie group, and in terms of a sublaplacian. We then show how to solve the question of when a Sobolev space is an algebra on a general Lie group, where the Sobolev space is defined in terms of a sublaplacian.   Then we discuss a number of open problem that arose from this work, which is in collaboration with M. Vallarino.

Host: John McCarthy