(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 ?