Projective multiresolution analyses for dilations in higher dimensions

dc.creatorPacker, Judith A.
dc.date2005-02-25
dc.date.accessioned2026-07-07T05:17:31Z
dc.date.available2026-07-07T05:17:31Z
dc.descriptionWe continue the study of projective module wavelet frames corresponding to diagonal dilation matrices on $\mathbb R^n$ with integer entries, focusing on the construction of a projective multi-resolution analysis corresponding to dilations whose domains are finitely generated projective modules over continuous complex-valued functions on $n$-tori, $n\geq 3$. We are able to generalize some of these results to dilation matrices that are conjugates of integral diagonal dilation matrices by elements of $SL(n,\mathbb Z).$ We follow the method proposed by the author and M. Rieffel, and are able to come up with examples of non-free projective module wavelet frames which can be described via this construction. As an application of our results, in the case $n=3,$ when the dilation matrix is a constant multiple of the identity, we embed every finitely generated module as an initial module.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/math/0502557
dc.identifierhttp://arxiv.org/abs/math/0502557
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74334
dc.subjectFunctional Analysis
dc.subjectK-Theory and Homology
dc.subjectPrimary 46L99; Secondary 42C15, 46H25, 19M05
dc.titleProjective multiresolution analyses for dilations in higher dimensions
dc.typetext

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