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Representation of the Dirac Delta Function

Please see the attached file for the fully formatted problems.

Show that

is a representation of the Dirac S-function.

and let f(x) be a function which is piecewise continuous on [?a, a], in particular,

(Dirac delta function)

one must show that

One way of doing this is to follow the approach used to obtain an analogous result in the process of establishing the validity of the Fourier series theorem, and then use the result that


Solution Summary

A Fourier series theorem is used in a proof involving the Dirac delta function. The solution is well presented.