Fourier Frames for the Cantor-4 Set

作者：Picioroaga Gabriel^*; Weber Eric S

来源：Journal of Fourier Analysis and Applications, 2017, 23(2): 324-343.

DOI：10.1007/s00041-016-9471-0

• Fourier series
• Frames
• Fractals
• Iterated function system
• Cuntz algebra

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 two 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.

• 出版日期2017-4