@article{article_718157, title={Covariant and Contravariant Symbols of Operators on $l^{2}(\mathbb{Z})$}, journal={Fundamental Journal of Mathematics and Applications}, volume={3}, pages={116–124}, year={2020}, DOI={10.33401/fujma.718157}, author={Elmabrok, Abdelhamid S}, keywords={Bounded, Compact and finite rank operators, Covariant and contravariant symbols of operators, Wavelet transformation}, abstract={<p style="text-align:justify;"> <span style="font-size:14px;">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, Uniquenes </span>s, Boundedness, Compactnessi and Finite rank) of these operators and reformulated some know results in terms of wavelet transform (covariant and contravariant symbols). <span style="font-size:14px;"> </span> </p>}, number={2}, publisher={Fuat USTA}