= Spectral accuracy
A <spectral method> has <spectral accuracy> for a class of smooth data when its error decreases faster than any fixed inverse power of the truncation size. For periodic <Fourier series>, this follows from arbitrarily many integrations by parts when every derivative matches across the periodic boundary. An analytic periodic extension to a complex strip gives exponential coefficient decay. Analyticity inside one period and matching only endpoint values do not suffice: a jump in a derivative of the periodic extension yields algebraic decay instead.
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