Some unexpected behaviors of operators with small time-frequency dispersion
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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