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P1: (H*δ)'=?, where H is the heavisede distrobution and δ is diracs distributin. So I tried liek this : <(H*δ)',φ>=-<H*δ,φ'>=-<δ,<H,φ'>>, <H,φ'>=∫φ'dx=φ => -<δ,φ>=<(H*δ)',φ> => (H*δ)'=δ. This is the result given so I think it's OK.

P2ere is my real problem, here I have doubts-unclearityes so it looks like this :

F[δ*δ]=?, Where F[] is the Fourier transform. My solution: <F[δ*δ],φ>=<δ*δ,F[φ]>=

<δ,<δ,F[φ]>, <δ,F[φ]>=F[φ](0)=∫φe^0dx=∫φdx=∫1φdx=<T1,φ> =>

<δ,<δ,F[φ]>=<δ,<T1,φ>> So I by definition <δ,φ>=φ(0) so this is<T1,φ>(0) but I don't really know what tis means... does it mean <T1,φ>? Because if it means this then the solution given by the book is correct and is T1, but if it is not or even if it is could anyone tell me why is it like this ? Because in ∫φdx(0) I don't really see the reason.