Seminario

Seminario Q-Math

Sampling (reconstructing) Hilbert-Schmidt operators: Why and how to do it?

Ponente:  Antonio García (UC3M)
Fecha:  martes 26 de octubre de 2021 - 13:00
Lugar:  Room 2.2.D08 (Universidad Carlos III de Madrid)

Resumen:

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 analogous sampling formulas. The key point here is the use of the Weyl transform (or the Kohn-Nirenberg transform), a unitary mapping between the space of square integrable functions in the phase space \(\mathbb{R}^d\times \widehat{\mathbb{R}}^d\) and the Hilbert space of Hilbert-Schmidt operators on \(L^2(\mathbb{R}^d) \), which permits to take advantage of some well established sampling results. A practical motivation for this sampling problem is given by the channel estimation problem in wireless communications.