2. Let f: R-R be defined by f(x) = e-le| (a). Show that f exists. (b). Calculate f. (c). Use the inversion theorem to find cos t 1+ 12 dt Let f € L'(R). The Fourier transform of f is the function ĵ(x) := f(t)e-it dt
2. Let f: R-R be defined by f(x) = e-le| (a). Show that f exists. (b). Calculate f. (c). Use the inversion theorem to find cos t 1+ 12 dt Let f € L'(R). The Fourier transform of f is the function ĵ(x) := f(t)e-it dt
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Transcribed Image Text:2. Let f: R R be defined by
f(x) = e-lei
%3D
(a). Show that ĵ exists.
(b). Calculate f.
(c). Use the inversion theorem to find
cos t
1+12dt
Let f E L'(R). The Fourier transform of f is the function
1
Î(x) :=
-ixt
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