19. Fourier Transform - Probability
Tutorial 19: Fourier Transform 2 1. Show that for all u2R,themapx! (u;x) is measurable.2. Show that for all u2R,wehave: Z +1 1 j (u;x)jdx= p 2ˇ<+1 and conclude that ˚is well de ned. 3. Let u2R and (u n) n 1 be a sequence in R converging to u. Show that ˚(u n)!˚(u) and conclude that ˚is continuous. 4. Show that: Z +1 0 xe x2=2dx=1 5. Show that for all u2R,wehave: Z
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