7 papers
Sampling in -shift-invariant subspaces of Hilbert-Schmidt operators on
Antonio G. García
The translation of an operator is defined by using conjugation with time-frequency shifts. Thus, one can define -shift-invariant subspaces of Hilbert-Schmidt operators, finitely…
Sampling in the range of the analysis operator of a continuous frame having unitary structure
Antonio G. García
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary repre…
Average sampling in certain subspaces of Hilbert-Schmidt operators on
Antonio G. García
The concept of translation of an operator allows to consider the analogous of shift-invariant subspaces in the class of Hilbert-Schmidt operators. Thus, we extend the concept of av…
Convolution systems on discrete abelian groups as a unifying strategy in sampling theory
Antonio G. García, Miguel A. Hernández-Medina, Gerardo Pérez-Villalón
A regular sampling theory in a multiply generated unitary invariant subspace of a separable Hilbert space is proposed. This subspace is associated to a unitary repres…
Knit product of finite groups and sampling
Antonio G. García, Miguel A. Hernández-Medina, Albert Ibort
A finite sampling theory associated with a unitary representation of a finite non Abelian group on a Hilbert space is stablished. The non Abelian group is…
Semi-direct product of groups, filter banks and sampling
Antonio G. García, Miguel A. Hernández-Medina, Gerardo Pérez-Villalón
An abstract sampling theory associated to a unitary representation of a countable discrete non abelian group , which is a semi-direct product of groups, on a separable Hilbert s…