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absolutely convergent Fourier applied belongs to Lt Bessel inequality class of functions complete the proof const constant convergent Fourier series converges absolutely defined definition denumerable normal set denumerable set equivalent established everywhere finite interval finite number finite range follows formula Fourier integral Fourier series Fourier transform function f(x harmonic analysis Hence Iff(x infinite J-oo Kt(x Lambert series Lebesgue integral Lemma 6u Let f(x let us notice let us put lim f lim sup limited total variation linear lira measurable function Minkowski inequality modulus monotone increasing non-negative null set number of dimensions number of f(x obtain periodic functions Plancherel theorem polynomial positive proof of theorem proposition prove real numbers Riemann Riesz-Fischer theorem Schwarz inequality sequence set of points step-function summable Tauberian theorem tends term by term theorem 15 theorem 22 theory true uniformly values vanish Wiener zero
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