Appendix
Theory of Distributions
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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