On regular families of cardinal interpolators and multiresolution analyses

2014/06/24 by Jeff Ledford, Ledford, Jeff
Mathematics · #41A15 #41A63 #42C15 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA #msc:41A15 #msc:41A63 #msc:42C15

paper · pdf · doi:10.48550/arxiv.1406.6244

keywords: multiresoultion analyses, splines, multiquadric 7 pages

arxiv created 2014/06/24 · arxiv updated 2014/06/25

Abstract

In this short note, we investigate the relationship between so-called regular families of cardinal interpolators and multiresolution analyses. We focus our studies on examples of regular families of cardinal interpolators whose Fourier transform is unbounded at the origin. In particular, we show that when this is the case there is a multiresolution analysis corresponding to each member of a regular family of cardinal interpolators.

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