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(1) What are all positive Schwartz Functions on $\mathbb R$ whose Fourier Transform is positive ?

(2) What are all Schwartz Functions on $\mathbb R$ whose Fourier Transform is positive ?

(3) What are all positive Schwartz Functions on $\mathbb R$ whose Fourier Transform is non-negative ?

(4) What are all Schwartz Functions on $\mathbb R$ whose Fourier Transform is non-negative ?

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