Jordy Timo van Velthoven

activity

20172026

most citedSmooth lattice orbits of nilpotent groups and strict comparison of projections

9 citations · 16 across the 27 of their papers we have counts for

collaborators

33 papers

math.FA2026

A Balian-Low theorem for nilpotent Lie groups

Ulrik Enstad, Jordy Timo van Velthoven

We prove strict necessary density conditions for smooth coherent frames and Riesz sequences in the orbit of a connected, simply connected, nilpotent Lie group. This extends previou…

math.FA2026

Linear dependence of time-frequency shifts of a Schwartz function

Markus Faulhuber, Philipp Petersen, Jordy Timo van Velthoven +1

We show that a finite number of time-frequency shifts of a Schwartz function can be linearly dependent. This disproves the so-called HRT conjecture of Heil, Ramanathan, and Topiwal…

math.FA2026

Triebel-Lizorkin spaces and expansive matrices

Marcin Bownik, Jordy Timo van Velthoven

We survey recent classification theorems for expansive matrices that generate the same anisotropic homogeneous Triebel-Lizorkin function space or sequence space. The function space…

math.FA2026

Coherent frames with zero Beurling density

Ingrid Beltita, Jordy Timo van Velthoven

We show the existence of a coherent frame in the orbit of a connected, simply connected unimodular solvable Lie group of exponential growth for which the lower Beurling density of…

math.CA2026

On the Calderón sum formula for wavelet systems

Ulrik Enstad, Jordy Timo van Velthoven

We show that the Calderón sum formula for orthonormal wavelet bases holds for arbitrary dilation and translation matrices under a mild condition on the wavelet function. This parti…

math.CA2025

Exponential frames and Riesz sequences at the critical density

Ulrik Enstad, Jordy Timo van Velthoven

We characterize exponential systems on sets of finite measure that form a frame or a Riesz sequence at the critical density. Namely, they are precisely those systems for which the…

math.FA2025

Frame redundancy and Beurling density

Marcin Bownik, Jordy Timo van Velthoven

We show that the frame measure function of a frame in certain reproducing kernel Hilbert spaces on metric measure spaces is given by the reciprocal of the Beurling density of its i…

math.FA2025

Density conditions with stabilisers for lattice orbits of discrete series representations

Jordy Timo van Velthoven

This note provides elementary proofs for necessary density conditions for frames and Riesz sequences in the lattice orbit of a discrete series representation that involve the proje…

math.FA2025

Besov and Triebel-Lizorkin spaces on homogeneous groups

Guorong Hu, David Rottensteiner, Michael Ruzhansky +1

This paper develops a theory of Besov spaces $B ˙_{p, q}^{σ} (N)$ and Triebel-Lizorkin spaces $F ˙_{p, q}^{σ} (N)$ on an arbitrary homogeneous group $N$ for the…

math.CA2024

On exponential frames near the critical density

Marcin Bownik, Jordy Timo van Velthoven

Given a relatively compact set $Ω \subseteq R$ of Lebesgue measure $∣Ω∣$ and $ε > 0$ , we show the existence of a set $Λ \subseteq R$ of uniform density $D…

math.CA2024

Discrete Triebel-Lizorkin spaces and expansive matrices

Jordy Timo van Velthoven, Felix Voigtlaender

We provide a characterization of two expansive dilation matrices yielding equal discrete anisotropic Triebel-Lizorkin spaces. For two such matrices $A$ and $B$ , it is shown that $\…

math.RT2024

Characteristically nilpotent Lie groups with flat coadjoint orbits

Dietrich Burde, Jordy Timo van Velthoven

We study the existence of certain characteristically nilpotent Lie algebras with flat coadjoint orbits. Their connected, simply connected Lie groups admit square-integrable represe…

math.FA2024

Counting function estimates for coherent frames and Riesz sequences

Effie Papageorgiou, Jordy Timo van Velthoven

We prove various estimates for the asymptotics of counting functions associated to point sets of coherent frames and Riesz sequences. The obtained results recover the necessary den…

math.RT2024

Symplectic projective orbits of unimodular exponential Lie groups

Ingrid Beltita, Jordy Timo van Velthoven

For an exponential Lie group $G$ and an irreducible unitary representation $(π, H_{π})$ of $G$ , we consider the natural action defined by $π$ on the projective space of $\ma…

math.CA2023

Classification of anisotropic local Hardy spaces and inhomogeneous Triebel-Lizorkin spaces

Jordy Timo van Velthoven, Felix Voigtlaender

This paper provides a characterization of when two expansive matrices yield the same anisotropic local Hardy and inhomogeneous Triebel-Lizorkin spaces. The characterization is in t…

math.CA2023

Hardy spaces and dilations on homogeneous groups

Tommaso Bruno, Jordy Timo van Velthoven

On a homogeneous group, we characterize the one-parameter groups of dilations whose associated Hardy spaces in the sense of Folland and Stein are the same.

math.FA2023

Linear independence of coherent systems associated to discrete subgroups

Ulrik Enstad, Jordy Timo van Velthoven

This note considers the finite linear independence of coherent systems associated to discrete subgroups. We show by simple arguments that such coherent systems of amenable groups a…

math.FA2022

Classification of anisotropic Triebel-Lizorkin spaces

Sarah Koppensteiner, Jordy Timo van Velthoven, Felix Voigtlaender

This paper provides a classification theorem for expansive matrices $A \in GL (d, R)$ generating the same anisotropic homogeneous Triebel-Lizorkin space $\dot{\mat…

math.FA2022★ 1 cited

Overcompleteness of coherent frames for unimodular amenable groups

Martijn Caspers, Jordy Timo van Velthoven

This paper concerns the overcompleteness of coherent frames for unimodular amenable groups. It is shown that for coherent frames associated with a localized vector a set of positiv…

math.FA2022★ 2 cited

Coherent systems over approximate lattices in amenable groups

Ulrik Enstad, Jordy Timo van Velthoven

Let $G$ be a second-countable amenable group with a uniform $k$ -approximate lattice $Λ$ . For a projective discrete series representation $(π, H_{π})$ of $G$ of formal degre…

math.FA2022

Anisotropic Triebel-Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, II

Sarah Koppensteiner, Jordy Timo van Velthoven, Felix Voigtlaender

Continuing previous work, this paper provides maximal characterizations of anisotropic Triebel-Lizorkin spaces $F ˙_{p, q}^{α}$ for the endpoint case of $p = \infty$ and…

math.FA2022

Coorbit spaces associated to quasi-Banach function spaces and their molecular decomposition

Jordy Timo van Velthoven, Felix Voigtlaender

This paper provides a self-contained exposition of coorbit spaces associated to integrable group representations and quasi-Banach function spaces, and at the same time extends and…

math.FA2021★ 4 cited

On sufficient density conditions for lattice orbits of relative discrete series

Ulrik Enstad, Jordy Timo van Velthoven

This note provides new criteria on a unimodular group $G$ and a discrete series representation $(π, H_{π})$ of formal degree $d_{π} > 0$ under which any lattice $Γ \leq G$ wit…

math.FA2021

Density conditions with stabilizers for lattice orbits of Bergman kernels on bounded symmetric domains

Martijn Caspers, Jordy Timo van Velthoven

Let $π_{α}$ be a holomorphic discrete series representation of a connected semi-simple Lie group $G$ with finite center, acting on a weighted Bergman space $A_{α}^{2} (Ω)$ on a bounded s…