Joseph D. Lakey

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In this paper we construct IR n-valued biorthogonal, compactly supported multiwavelet families such that one of the biorthogo-nal pairs consists of divergence-free vector wavelets. The construction is based largely on Lemari e's idea of multiresolution analyses intertwined by diierentiation. We show that this technique extends nontrivially to multiwavelets(More)
The Hardy space H 1 ρr (R n) consists of all divergence free r-form distributions f whose non-tangential maximal functions are in L 1 (R n). We say that a system of singular integrals characterizes H 1 ρr (R n) if this space consists precisely of those divergence-free r-form distributions f whose images under the singular integral operators are integrable.(More)
We refer to eigenfunctions of the kernel corresponding to truncation in a time interval followed by truncation in a frequency band as bandpass prelates (BPPs). We prove frame bounds for certain families of shifts of bandpass prolates, and we numerically construct dual frames for finite dimensional analogues. In the continuous case, the corresponding(More)