Sampling in $ \Lambda $-shift-invariant subspaces of Hilbert-Schmidt operators on $ L^2(\mathbb{R}^d) $

<p style='text-indent:20px;'>The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define <inline-formula><tex-math id="M3">\begin{document}$ \Lambda $\end{document}</tex-math></inline-formula>-shift-invariant subspaces Hilbert-Schmidt operators, finitely generated, respect to a lattice id="M4">\begin{document}$ $\end{document}</tex-math></inline-formula> in id="M5">\begin{document}$ \mathbb{R}^{2d} $\end{document}</tex-math></inline-formula>. These spaces be seen as generalization classical shift-invariant square integrable functions. Obtaining sampling results for these appears natural question that motivated the problem channel estimation wireless communications. are obtained light frame theory separable Hilbert space.</p>