Authored website post credited to Terence Tao and published 6 April 2009. Its course category is 245C, Real Analysis; the byline applies to this post, not to a separately published book of every course resource.
Cited passages: §3, Definition 32 and Exercise 54: Schwartz hypotheses and Poisson summation on the integer lattice; §3, Exercise 41: transform of a scaled Gaussian; put r=1/sqrt(a) and adjust its prefactor.
Additional locator: section 2, the constant character and Corollary 22, Fourier expansion on compact abelian groups with probability Haar measure. The zero coefficient is the average against the constant character. terrytao.wordpress.com/2009/04/06/the-fourier-transform/

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