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Appendix
The Theory of Distributions is the mathematical framework which underlies the generalized Fourier Transforms.
Notice two things:
- is linear
-
With these definitions, we can now define the Dirac delta in terms of distrubions. Let
be any function such that
Define
to be
Now we can defined
which is the property of the Dirac Delta we want. Now we can define the generalized Fourier Transform in terms of distributions.
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