In this problem set define the Fourier transform of a function f el(R) by f(x) = SR f(t)e-2rita dt (10) Show that if f
Posted: Thu May 12, 2022 12:46 pm
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(10) Show that if f = S(R) then f (its Fourier transform) is also in S(R).
(Schwartz space) The Schwartz space on R, S(R) is the set of all
C functions f such that its derivatives f' f (2),...,f(k) are all rapidly decreasing in the sense that supreR |2|4|f'(x) < for all k, 120.