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If a function belongs to G(R) but has points that are jump discontinuities, it's Fourier transform will not belong to G(R).
But would it be correct to claim that if a function in G(R) is continuous than its Fourier transform also belongs to G(R)? I guess it's not true, but can someone suggest a counterexample?
Thanks.
But would it be correct to claim that if a function in G(R) is continuous than its Fourier transform also belongs to G(R)? I guess it's not true, but can someone suggest a counterexample?
Thanks.