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    Fourier transform in distribution sense

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    Please solve problem number 1 on the attached PDF file

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    a) Let's consider a test function D; we have to compute the limit of the inner product which defines a distribution as a linear and continuous functional:
    ( 1)
    ( 2)
    we will have: ( 3)
    Let's put

    Solution Summary

    Fourier transform in distribution sense is evaluated.