Admissible Vectors of a Covariant Representation of a Dynamical System

Abstract

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system. In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to a uniform lattice of $G$.

Keywords

• Admissible vector
• Covariant representation
• Dynamical system