Fourier bases and Fourier frames on self-affine measures
Functional Analysis
2016-02-16 v1
Abstract
This paper gives a review of the recent progress in the study of Fourier bases and Fourier frames on self-affine measures. In particular, we emphasize the new matrix analysis approach for checking the completeness of a mutually orthogonal set. This method helps us settle down a long-standing conjecture that Hadamard triples generates self-affine spectral measures. It also gives us non-trivial examples of fractal measures with Fourier frames. Furthermore, a new avenue is open to investigate whether the Middle Third Cantor measure admits Fourier frames.
Cite
@article{arxiv.1602.04750,
title = {Fourier bases and Fourier frames on self-affine measures},
author = {Dorin Ervin Dutkay and Chun_Kit Lai and Yang Wang},
journal= {arXiv preprint arXiv:1602.04750},
year = {2016}
}