Coorbit spaces with voice in a Fréchet space

Abstract

We set up a new general coorbit space theory for reproducing representations of a locally compact second countable group $G$ that are not necessarily irreducible nor integrable. Our basic assumption is that the kernel associated with the voice transform belongs to a Fréchet space $\mathcal{T}$ of functions on $G$, which generalizes the classical choice $\mathcal{T}=L_w^1(G)$. Our basic example is $\mathcal{T}={\bigcap }_{p\in (1,+\infty )}{L}^p(G)$, or a weighted versions of it. By means of this choice it is possible to treat, for instance, Paley-Wiener spaces and coorbit spaces related to Shannon wavelets and Schrödingerlets.

52 pages, 1 figures

References in corpus (1)

• Generalized coorbit space theory and inhomogeneous function spaces of Besov-Lizorkin-Triebel type