Question: really need help with problem 1. We are using Fourier Inversion, and Heisenberg for reference. (1) Show that if fe S(R ), then f is

really need help with problem 1. We are using Fourier Inversion, and Heisenberg for reference.

(1) Show that if fe S(R" ), then f is uniformly continuous on R". (2) Let f E S(R). Prove the following identities: (i) F[(-2mix)f()](5) = (f)'({) for all multi-indices a. (ii) F[f(a + h)](8) = f(()e2mine for all he R. (iii) F[f()](8) = x-If for all > > 0

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