2019/07/01 by Helge Knutsen, Knutsen, Helge
Computer Science · Earth and Planetary Sciences · Mathematics · #47A30 #47A75 #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Underwater Acoustics Research
paper · pdf · doi:10.48550/arxiv.1907.00848
openalex publication_date 2019/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study Daubechies' time-frequency localization operator, which is characterized by a window and weight function. We consider a Gaussian window and a spherically symmetric weight as this choice yields explicit formulas for the eigenvalues, with the Hermite functions as the associated eigenfunctions. Inspired by the fractal uncertainty principle in the separate time-frequency representation, we define the n-iterate spherically symmetric Cantor set in the joint representation. For the n-iterate Cantor set, precise asymptotic estimates for the operator norm are then derived up to a multiplicative constant.