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arXiv · 2210.07915

Some unexpected behaviors of operators with small time-frequency dispersion

Dae Gwan Lee
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Abstract

We study the approximation properties of pseudo-differential operators with small time-frequency dispersion, meaning that their spreading functions are supported in a small neighborhood of the origin. It is commonly assumed that for such operators $H$, the output $Hf$ can differ only a little from a scalar multiple of the input $f$. However, we disprove this heuristic statement, hence revealing some unexpected behaviors of such operators.

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Dae Gwan Lee. 2022-10-14. Some unexpected behaviors of operators with small time-frequency dispersion. https://arxiv.org/abs/2210.07915

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