Convergence of mock Fourier series

By Robert S. Strichartz. 2006

159 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f664ddeb4dc79091d71c184aca746845e3db80f3

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In Applied Mathematics

1. Xin-Rong Dai
2. Xinggang He
3. Chun-Kit Lai
4. Li-Xiang An
5. Qiyu Sun
6. Xiaoye Fu
7. Ka-Sing Lau
8. Dorin Ervin Dutkay

In Mathematical Physics

1. Xin-Rong Dai
2. Xinggang He
3. Chun-Kit Lai
4. Li-Xiang An
5. Qiyu Sun
6. Ka-Sing Lau
7. Xiaoye Fu
8. Dorin Ervin Dutkay

Citations in the corpus

• Spectral measures generated by arbitrary and random convolutions (2015, background): “ral [HL08, Dai12] and classifying their possible spectra [DHS09, DHL13]. It was surprising to find that the convergence of the associated Fourier series is uniform in the space of continuous functions [Str06]. All the constructions of singular spectral measures, in the literature, to the best of our ”
• Exponential spectra in L2(μ) (2013, background): “This raises the very interesting question on the existence of an exponential Riesz basis or a Fourier frame for such measures, and more generally for the self-similar measures [15,16,6,25, 10].”
• Weak convergence and spectrality of infinite convolutions (2022, background): “[51] R. Strichartz, Convergence of mock Fourier series, J. Anal.”
• Spectrality of Self-Similar Tiles (2013, background): “The problem also led to the study of spectral property of discrete integer tiles [12,33,40] and the Cantor-type singularly continuous measures [1,4–6,8,9,18,23,29,41].”
• Non-spectral problem for a class of planar self-affine measures (2008, background): “The spectral self-affine measure problem at the present day consists in determining conditions under which μM,D is a spectral measure, and has been studied in the papers [2–6,18,23,25,27,28,32] (see also [33,34] for the main goal).”
• Spectral measures with arbitrary Hausdorff dimensions (2014, background): “Fourier serie s corresponding to di fferent spectra could have completely di fferent convergence rate [8, 30].”
• Spectra of Cantor measures (2014, background): “A spectral measure may admit various spectra and the Fourier expansion associated with distinct spectra could have completely di fferent convergence property [6,27].”
• Number theory problems from the harmonic analysis of a fractal (2014, background): “bert space L2(µ) has an orthonormal basis formed with exponential functions, i.e., a Fourier basis, E(Γ 0) := {eλ : λ ∈ Γ 0} where (1.3) Γ 0 := ( Xn k=0 4kl k : lk ∈ {0,1},n ∈ N ) . Later, Strichartz [Str06] proved that these Fourier series have better convergence properties than their classical cou”