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math.CA2025
The Fourier Ratio and complexity of signals
K. Aldaleh, W. Burstein, G. Garza +12
We study the Fourier ratio of a signal , \[ \mathrm{FR}(f)\ :=\ \sqrt{N}\,\frac{\|\widehat f\|_{L^1(μ)}}{\|\widehat f\|_{L^2(μ)}} \ =\ \frac{\|\widehat…
math.CA2024
Buffon Needle Problem Over Convex Sets
M. Dannenberg, W. Hagerstrom, G. Hart +4
We solve a variant of the classical Buffon Needle problem. More specifically, we inspect the probability that a randomly oriented needle of length originating in a bounded conv…