مشخصات پژوهش

In this paper, we first characterize the boundedness of the weighted translation pre-frame operator, namely, $ T_{\omega,\varphi,f} $ and its adjoint. Then, we identify the relation between the adjoint of $ T_{\omega,\varphi,f} $ and the translation frame operator which is denoted by $ S_{\omega,\varphi,f} $. Basically, all results are obtained by using the conditional expectation properties.