New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis

Abstract

We study function spaces that are related to square-integrable, irreducible, unitary representations of several low-dimensional nilpotent Lie groups. These are new examples of coorbit theory and yield new families of function spaces on $\mathbb{R}^d $. The concrete realization of the representation suggests that these function spaces are useful for generalized time-frequency analysis or phase-space analysis.