On regular families of cardinal interpolators and multiresolution analyses

TL;DR

This paper explores the connection between regular families of cardinal interpolators with unbounded Fourier transforms at zero and their associated multiresolution analyses, revealing a correspondence for each family member.

Contribution

It demonstrates that regular families of cardinal interpolators with unbounded Fourier transforms at zero can be linked to multiresolution analyses, expanding understanding of their relationship.

Findings

Multiresolution analysis exists for each member of the regular family.

Fourier transform unboundedness at zero is key to the analysis.

Establishes a link between interpolator families and multiresolution structures.

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.