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The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.

2 votes

Is there a Poisson Summation formula for imprimitive Dirichlet characters?

Yes, of course. Poisson summation formula has nothing to do with characters. If χ is any periodic function, all you need to do is to replace χ̅ by the discrete Fourier Transform of χ.
Ilya Zakharevich's user avatar