13 papers
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…
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…
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…
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 and , it is shown that $\…
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 part…
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…