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arXiv · 1503.01763

Fourier Frames for the Cantor-4 Set

Gabriel Picioroaga·Eric S. Weber
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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.

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BibTeXRIS

Gabriel Picioroaga, Eric S. Weber. 2015-03-05. Fourier Frames for the Cantor-4 Set. https://arxiv.org/abs/1503.01763

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