Journal of Fractal Geometry

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Volume 4, Issue 3, 2017, pp. 305–327
DOI: 10.4171/JFG/52

Published online: 2017-09-12

Non-spectral fractal measures with Fourier frames

Chun-Kit Lai[1] and Yang Wang[2]

(1) San Francisco State University, USA
(2) Hong Kong University of Science and Technology, China

We generalize the compatible tower condition given by Strichartz to the almost-Parseval-frame tower and show that non-trivial examples of almost-Parseval-frame tower exist. By doing so, we demonstrate the first singular fractal measure which has only finitely many mutually orthogonal exponentials (and hence it does not admit any exponential orthonormal bases), but it still admits Fourier frames.

Keywords: Fourier frame, frame spectral measures, fractal measures, almost Parseval frames, spectra

Lai Chun-Kit, Wang Yang: Non-spectral fractal measures with Fourier frames. J. Fractal Geom. 4 (2017), 305-327. doi: 10.4171/JFG/52