Though we know for any $f\in L^1(R)$, its Fourier transform $\hat{f}\in C_0$, what can we say about its differentiability? I'm trying to construct an example to make both $f,\hat{f}\in L^1$ but $\hat{f}$ is nowhere differentiable. Is this possible?
2026-04-03 01:23:12.1775179392
Will the differentiability of Fourier transform be very bad?
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