6 papers
Riesz sequences near the critical density
Marcin Bownik, Jordy Timo van Velthoven
We construct Riesz sequences whose Beurling density is arbitrary close to the critical density in the setting of reproducing kernel Hilbert spaces on metric measure spaces. In part…
Uniform discretization of continuous frames
Marcin Bownik, Pu-Ting Yu
Let be an infinite-dimensional separable Hilbert space and let be a metric measure space satisfying the doubling and upper Alhfors regularity conditions at small scal…
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…
Meyer wavelets for rational dilations
Marcin Bownik
We show the existence of smooth band-limited multiresolution analysis (MRA) for any expansive dilation with real entries in any spatial dimension. We then prove the existence of or…
On exponential frames near the critical density
Marcin Bownik, Jordy Timo van Velthoven
Given a relatively compact set of Lebesgue measure and , we show the existence of a set of uniform density $D…
Selector form of Weaver's conjecture, Feichtinger's conjecture, and frame sparsification
Marcin Bownik
We show an extension of a probabilistic result of Marcus, Spielman, and Srivastava, which resolved the Kadison-Singer problem, for block diagonal positive semidefinite random matri…