Question: How do I complete the following two exercises? The goal is to show that the Fourier transform is not surjective. Problem 25.8. This problem gives

How do I complete the following two exercises? The goal is to show that the Fourier transform is not surjective.

How do I complete the following two exercises? The goal is to

Problem 25.8. This problem gives a proof that the Fourier transformA: L1 > ODOR) is not surjective. a) Draw a picture of hn :2 1[n,n] * 1[_1,1] and determine its ODOR) norm. b) Show that ha is, up to a multiplicative constant independent of n, the Fourier transform of the L1 function sin 2m: sin 27mm fn = (Hint: you can compute integrals, or use the L1 inversion theorem.) 1:2

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