22 citations · 26 across the 12 of their papers we have counts for
13 papers
From Fractional to Set Tilings for Pairs of Lattices
Darrin Speegle
We generalize a theorem of Isbell asserting that every countably infinite doubly stochastic matrix has a positive generalized diagonal. As an application, we prove a support-reduct…
Are MSF wavelets minimally supported?
Marcin Bownik, Ziemowit Rzeszotnik, Darrin Speegle
Larson's problem asks ``Must the support of the Fourier transform of a wavelet contain a wavelet set?". We give an affirmative answer to a non-measurable variant of this question b…
Strictly Expansive Matrices
Darrin Speegle
If is an integer valued, strictly expansive matrix, then there exists an orthonormal -wavelet whose Fourier transform is compactly supported and smooth. We show that strongl…
Simultaneous dilation and translation tilings of
Marcin Bownik, Darrin Speegle
We solve the wavelet set existence problem. That is, we characterize the full-rank lattices and invertible matrices for which there exists a…
The discretization problem for continuous frames
Daniel Freeman, Darrin Speegle
We characterize when a coherent state or continuous frame for a Hilbert space may be sampled to obtain a frame, which solves the discretization problem for continuous frames. In pa…
Improved bounds in Weaver and Feichtinger Conjectures
Marcin Bownik, Peter G. Casazza, Adam W. Marcus +1
We sharpen the constant in the conjecture of Weaver \cite{We}, which was validated by Marcus, Spielman, and Srivastava \cite{MSS} in their solution of the Kadison--Singer pr…