81 citations · 338 across the 34 of their papers we have counts for
16 papers · 1 filter
Sampling in the shift-invariant space generated by the bivariate Gaussian function
José Luis Romero, Alexander Ulanovskii, Ilya Zlotnikov
We study the space spanned by the integer shifts of a bivariate Gaussian function and the problem of reconstructing any function in that space from samples scattered across the pla…
Random periodic sampling patterns for shift-invariant spaces
Jorge Antezana, Diana Carbajal, José Luis Romero
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 sample…
Eigenvalue estimates for Fourier concentration operators on two domains
Felipe Marceca, José Luis Romero, Michael Speckbacher
We study concentration operators associated with either the discrete or the continuous Fourier transform, that is, operators that incorporate a spatial cut-off and a subsequent fre…
Comment on "Affine density, von Neumann dimension and a problem of Perelomov"
José Luis Romero
We point out that the main theorem of Ref2 := [Adv. Math. 407, Article ID 108564, 22 p. (2022)] is included in the prior research survey Ref1 := [Expo. Math., 40(2), 265-301, 2022]…
Multiple sampling and interpolation in weighted Fock spaces of entire functions
Luis Alberto Escudero, Antti Haimi, José Luis Romero
We characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.
The density theorem for discrete series representations restricted to lattices
José Luis Romero, Jordy Timo van Velthoven
This article considers the relation between the spanning properties of lattice orbits of discrete series representations and the associated lattice co-volume. The focus is on the d…
On dual molecules and convolution-dominated operators
José Luis Romero, Jordy Timo van Velthoven, Felix Voigtlaender
We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the siz…
Balian-Low type theorems on homogeneous groups
Karlheinz Gröchenig, José Luis Romero, David Rottensteiner +1
We prove strict necessary density conditions for coherent frames and Riesz sequences on homogeneous groups. Let be a connected, simply connected nilpotent Lie group with a dila…
Invertibility of frame operators on Besov-type decomposition spaces
José Luis Romero, Jordy Timo van Velthoven, Felix Voigtlaender
We derive an extension of the Walnut-Daubechies criterion for the invertibility of frame operators. The criterion concerns general reproducing systems and Besov-type spaces. As an…
Sampling Theorems for Shift-invariant Spaces, Gabor Frames, and Totally Positive Functions
Karlheinz Gröchenig, José Luis Romero, Joachim Stöckler
We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors…
Density of Sampling and Interpolation in Reproducing Kernel Hilbert Spaces
Hartmut Führ, Karlheinz Gröchenig, Antti Haimi +2
We derive necessary density conditions for sampling and for interpolation in general reproducing kernel Hilbert spaces satisfying some natural conditions on the geometry of the spa…
Deformation of Gabor systems
Karlheinz Gröchenig, Joaquim Ortega-Cerdà, José Luis Romero
We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformat…
Frames adapted to a phase-space cover
Monika Dörfler, José Luis Romero
We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame…
Multi-window Gabor frames in amalgam spaces
Radu Balan, Jens G. Christensen, Ilya A. Krishtal +2
We show that multi-window Gabor frames with windows in the Wiener algebra are Banach frames for all Wiener amalgam spaces. As a byproduct of our results w…
Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces
Carlos Cabrelli, Ursula Molter, José Luis Romero
In this article we construct affine systems that provide a simultaneous atomic decomposition for a wide class of functional spaces including the Lebesgue spaces $L^p(\Rdst)$, $1<p<…
Characterization of coorbit spaces with phase-space covers
José Luis Romero
We show that coorbit spaces can be characterized in terms of arbitrary phase-space covers, which are families of phase-space multipliers associated with partitions of unity. This g…