Strong factorization theorem for smooth vectors of exponential solvable Lie group representations

TL;DR

This paper proves new strong factorization properties for smooth vectors in representations of exponential solvable Lie groups, extending the Dixmier-Malliavin theorem for nilpotent cases.

Contribution

It introduces improved factorization results for smooth vectors in exponential solvable Lie group representations, broadening the scope of the Dixmier-Malliavin theorem.

Findings

Enhanced factorization properties for smooth vectors

Extension of Dixmier-Malliavin theorem to exponential solvable groups

Applicable to representations on Fréchet spaces

Abstract

We establish new strong factorization properties for the smooth vectors of representations of exponential solvable Lie groups on Fr\'{e}chet spaces. In particular, our results improve upon the Dixmier-Malliavin factorization theorem for simply connected nilpotent Lie groups.