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.

References in corpus (1)

• Integrable wavelet transforms with abelian dilation groups

Cited by in corpus (3)

• Smooth lattice orbits of nilpotent groups and strict comparison of projections
• A Primer on Coorbit Theory -- From Basics to Recent Developments
• A Brief Introduction to the Feichtinger Algebra ${\mathbf{S}}_0(\mathbb{R})$