a) If f(x) is a function with unit area, show that the scaled and stretched function (1/a)f(x/a) also has unit area.

b) If F(w) is the Fourier transform of f(x), show that F(aw) is the Fourier transform of (1/a)f(x/a).

c) Show that part (b) implies that broadly spread functions have sharply peaked Fourier transforms near w=0, and vice versa.

b) If F(w) is the Fourier transform of f(x), show that F(aw) is the Fourier transform of (1/a)f(x/a).

c) Show that part (b) implies that broadly spread functions have sharply peaked Fourier transforms near w=0, and vice versa.

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