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

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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 1 (7.6 KiB) Viewed 37 times

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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 = 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.