1 citations · 2 across the 5 of their papers we have counts for
9 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…
Regular generalized sampling in T-invariant subspaces of a Hilbert space
Antonio G. García, María J. Muñoz-Bouzo, Gerardo Pérez-Villalón
A regular generalized sampling theory in some structured T-invariant subspaces of a Hilbert space H, where T denotes a bounded invertible operator in H, is established in this pape…
Modeling sampling in tensor products of unitary invariant subspaces
Antonio G. García, Alberto Ibort, María J. Muñoz-Bouzo
The use of unitary invariant subspaces of a Hilbert space is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of $L…
Towards a quantum sampling theory: the case of finite groups
Antonio G. García, Miguel A. Hernández-Medina, A. Ibort
Nyquist-Shannon sampling theorem, instrumental in classical telecommunication technologies, is extended to quantum systems supporting a unitary representation of a finite group …