Diana Carbajal

University of Vienna | UniWien · Faculty of Mathematics

We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a sampling strategy succeeds with high probability provided that the density of the sampling pattern exceeds the numbe...

We consider multi-variate signals spanned by the integer shifts of a set of generating functions with distinct frequency profiles and the problem of reconstructing them from samples taken on a random periodic set. We show that such a sampling strategy succeeds with high probability provided that the density of the sampling pattern exceeds the numbe...

Frames formed by orbits of vectors through the iteration of a bounded operator have recently attracted considerable attention, in particular due to its applications to dynamical sampling. In this article, we consider two commuting bounded operators acting on some Hilbert space $\mathcal{H}$. We completely characterize operators $T$ and $L$ and sets...

In this article, we characterize reducing and invariant subspaces of the space of square integrable functions defined in the unit circle and having values in some Hardy space with multiplicity. We consider subspaces that reduce the bilateral shift and at the same time are invariant under the unilateral shift acting locally. We also study subspaces...

In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define a new notion of diagonalization for these operators, which we call s-diagonalization. We give necessary and sufficient conditions on a bounded shift-preserving operator in order to be s-diagonalizable. These conditions a...

In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of L2(S) where S is a second countable LCA group. The subspaces where the operators act are invariant under the action of a group Γ which is a semi-direct product of a uniform lattice of S with a discrete group of automorphisms. T...

A correction to this paper has been published: https://doi.org/10.1007/s43670-021-00010-6

In this note, we solve the dynamical sampling problem for a class of shift-preserving operators L:V→V acting on a finitely generated shift-invariant space V. We find conditions on L and a finite set of functions of V so that the iterations of the operator L on the functions produce a frame generator set of V. This means that the integer translation...

In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of $L^2({\mathbf{R}})$ where ${\mathbf{R}}$ is a second countable LCA group. The subspaces where the operators act are invariant under the action of a group $\Gamma$ which is a semi-direct product of a uniform lattice of R with a...

In this note, we solve the dynamical sampling problem for a class of shift-preserving operators $L:V\to V$ acting on a finitely generated shift-invariant space $V$. We find conditions on $L$ and a finite set of functions of $V$ so that the iterations of the operator $L$ on the functions produce a frame generator set of $V$. This means that the inte...

In this note we study the structure of shift-preserving operators acting on a finitely generated shift-invariant space. We define a new notion of diagonalization for these operators, which we call s-diagonalization. We give necessary and sufficient conditions on a bounded shift-preserving operator in order to be s-diagonalizable. These conditions a...

We prove the existence of Riesz bases of exponentials of L 2 ( Ω ) L^2(\Omega ) , provided that Ω ⊂ R d \Omega \subset \mathbb {R}^d is a measurable set of finite and positive measure, not necessarily bounded, that satisfies a multi-tiling condition and an arithmetic property that we call admissibility . This property is satisfied for any bounded d...