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Errors and ambiguity in transition from Fourier series to Fourier integrals

Vladimir K. Petrov
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Abstract

Transition from Fourier series to Fourier integrals is considered and error introduced by ordinary substitution of integration for summing is estimated. Ambiguity caused by transition from discrete function to continuous one is examined and conditions under which this ambiguity does not arise are suggested.

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Vladimir K. Petrov. 2004-12-13. Errors and ambiguity in transition from Fourier series to Fourier integrals. https://arxiv.org/abs/hep-lat/0412019

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