Average sampling in certain subspaces of Hilbert&-Schmidt operators on L2(Rd)

The concept of translation of an operator allows to consider the analogue of shift-invariant subspaces in the class of Hilbert–Schmidt operators. Thus, we extend the concept of average sampling to this new setting, and we obtain the corresponding sampling formulas. The key point here is the use of the Weyl transform, a unitary mapping between the space of square integrable functions in the phase space Rd×Rˆd
and the Hilbert space of Hilbert–Schmidt operators on L2(Rd), which permits to take advantage of some well established sampling results.

average sampling; hilbert-schmidt operators; kohn-nirenberg transform; translation of operators; weyl transform

Average sampling in certain subspaces of Hilbert&-Schmidt operators on L2(Rd) Articles