Fourier Frames for the Cantor-4 Set
Functional Analysis
2015-03-06 v1
Abstract
The measure supported on the Cantor-4 set constructed by Jorgensen-Pedersen is known to have a Fourier basis, i.e. that it possess a sequence of exponentials which form an orthonormal basis. We construct Fourier frames for this measure via a dilation theory type construction. We expand the Cantor-4 set to a 2 dimensional fractal which admits a representation of a Cuntz algebra. Using the action of this algebra, an orthonormal set is generated on the larger fractal, which is then projected onto the Cantor-4 set to produce a Fourier frame.
Keywords
Cite
@article{arxiv.1503.01763,
title = {Fourier Frames for the Cantor-4 Set},
author = {Gabriel Picioroaga and Eric S. Weber},
journal= {arXiv preprint arXiv:1503.01763},
year = {2015}
}