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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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Solution Summary

Fourier transform in distribution sense is evaluated.

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Solution:

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)
Since
( 2)
we will have: ( 3)
Let's put
...

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