9.1 Let g = C(R). If F is any distribution acting on test functions in the...

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9.1 Let g = C(R). If F is any distribution acting on test functions in the class Co (R), we can define the product of g with F as a distribution; for any $ C(R), (gF, 4) = (F,g). (a) Why was this a reasonable definition? (b) Prove that |x| Ado the 3D Laplacian. = 6 So in the sense of distributions where x = R and A is 9.1 Let g = C(R). If F is any distribution acting on test functions in the class Co (R), we can define the product of g with F as a distribution; for any $ C(R), (gF, 4) = (F,g). (a) Why was this a reasonable definition? (b) Prove that |x| Ado the 3D Laplacian. = 6 So in the sense of distributions where x = R and A is