Gabor orthogonal bases and convexity

2017/08/21 by Alex Iosevich, Iosevich, Alex, Azita Mayeli +1 · 1 citation
Computer Science · Mathematics · Medicine · #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #math.CA #msc:42B10

paper · pdf · doi:10.48550/arxiv.1708.06397

arxiv created 2018/12/11 · arxiv updated 2018/12/12

Abstract

Let g(x)=χ_B(x) be the indicator function of a bounded convex set in \Bbb R^d, d≥ 2, with a smooth boundary and everywhere non-vanishing Gaussian curvature. Using a combinatorial appraoch we prove that if d ≠ 1 \mod 4, then there does not exist S ⊂ \Bbb R^2d such that \g(x-a)e^{2 πi x ⋅ b} \_{(a,b) ∈ S} is an orthonormal basis for L²(\Bbb R^d).

Citations

• The wavelet transform, time-frequency localization and signal analysis

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• Non-separable lattices, Gabor orthonormal bases and Tilings

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