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Density of the Set of Generators of Wavelet Systems
Carlos Cabrelli, Ursula Molter
Given a function in $ \LL^2(\R^d)$, the affine (wavelet) system generated by , associated to an invertible matrix and a lattice $\zG$, is the collection of functions $\{…
Local bases for refinable spaces
Carlos Cabrelli, Sigrid Heineken, Ursula Molter
We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particul…
Functions in Sampling Spaces
Cristina Blanco, Carlos Cabrelli, Sigrid Heineken
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is no…
Variations on the Theme of Journe's Lemma
Carlos Cabrelli, Michael Lacey, Ursula Molter +1
Journe's Lemma is a critical component of many questions related to the product theory of S.-Y. Chang and R. Fefferman. This article presents several different variants of…