Radix Representations, Self-Affine Tiles, and Multivariable Wavelets
Eva Curry
TL;DR
This paper explores the relationship between radix representations and self-affine tilings in multiple dimensions, demonstrating the existence of Haar-like multivariable wavelets for a broad class of dilation matrices.
Contribution
It establishes a novel connection between radix representations and self-affine tilings, leading to new results on multivariable wavelet existence.
Findings
Haar-like multivariable wavelets exist for all suitable dilation matrices
Radix representations are linked to self-affine tilings in R^n
New conditions for wavelet construction in multiple dimensions
Abstract
We investigate the connection between radix representations for Z^n and self-affine tilings of R^n. We apply our results to show that Haar-like multivariable wavelets exist for all dilation matrices that are sufficie
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