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absolutely convergent aeries analytic analytic function AneA approximation theorem arbitrarily arbitrary almost periodic basis chcose chosen coefficients consider continuous function converges uniformly corollary corres corresponding dces dense set Diriohlet eaoh einx exists expansion fact faot finite interval finite number following theorem follows immediately formula Fourier constants Fourier exponents Fourier series FT(x func function of period fundamental theorem funotiona given GT(x interval of length investigations iodic functions iodio kernel lation number Lebesgue integrable left half-plane limit equation linearly independent mean value theorem multiplication theorem normal orthogonal system obtain obviously ohcose olass Parseval equation Parseval's equation period 2n periodic funotions periodio prcof proof prove pure vibration purely periodic functions real numbers real variable relation relatively dense set of numbers simple Sn(x Stepanoff strip summable suoh theory tion translation number trigonometric polynomial uniformly convergent uniqueness theorem upper bound upper limit valid vanish identically whioh zero