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May 17 at 15:18 comment added Ribhu the Fourier transform of $f$ may not be defined. Note that $f$ belongs to a weighted $L^2$ space, so $f$ may not belong to $L^1(\mathbb{R})$ or $L^2(\mathbb{R})$.
S May 17 at 8:19 review First answers
May 17 at 9:27
S May 17 at 8:19 history answered Damien CC BY-SA 4.0