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1. (a) Show that f(x) = e defined on R is not a tempered distribution with its action on Schwartz class functions defined as the

1. (a) Show that f(x) = e defined on R is not a tempered distribution with its action on Schwartz class functions defined as the integration. (b) Prove that any polynomial is a tempered distribution. Then find the Fourier trans- form of f(x) = 2x3 - x - 1 as a tempered distribution

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