# The Dixmier-Malliavin theorem

## Noncommutative Geometry Seminar

## Meeting Details

For more information about this meeting, contact Allyson Borger, Nigel Higson.

**Speaker:** Michael Francis, Penn State

**Abstract:** In 1960, Ehrenpreis asked whether every smooth, compactly-supported function on n-dimensional Euclidean space can be expressed as the convolution of two such functions. The answer, as it turns out, is "yes" when n=1 and "no" when n is two or larger. In the positive direction, Dixmier-Malliavin showed in 1978 that, for any Lie group G, every smooth, compactly-supported function on G can be expressed as a finite sum of convolutions of such functions. Such "weak factorizations" are sufficient for many applications. In this talk, I will give an overview of Dixmier-Mallivin's theorem(s) and, time permitting, mention its relevance to some of my own work on foliation algebras.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 09/19/2019

**Time:** 2:30pm - 3:30pm