Covariant and Contravariant Symbols of Operators on $l^{2}(\mathbb{Z})$

Abstract

In this paper, we investigate covariant and contravariant symbols of operators generated by a representation of the integer group $\mathbb{Z}$. Then we describe some properties (Existence, Uniqueness, Boundedness, Compactnessi and Finite rank) of these operators and reformulated some know results in terms of wavelet transform (covariant and contravariant symbols).