Marcin Bownik

collaborators

4 papers

math.FA2026

Uniform discretization of continuous frames

Marcin Bownik, Pu-Ting Yu

Let $H$ be an infinite-dimensional separable Hilbert space and let $(X, d, I^¼)$ be a metric measure space satisfying the doubling and upper Alhfors regularity conditions at small sca…

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.CA2025

On exponential frames near the critical density

Marcin Bownik, Jordy Timo van Velthoven

Given a relatively compact set $I^c ◯ \subseteq R$ of Lebesgue measure $∣ I^c ◯ ∣$ and $ε > 0$ , we show the existence of a set $I^ \subseteq R$ of uniform density…

math.CA2025

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…