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A Riemann sum upper bound in the Riemann-Lebesque theorem

Maurice H. P. M. van Putten
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Abstract

The Riemann-Lebesque Theorem is commonly proved in a few strokes using the theory of Lebesque integration. Here, the upper bound $2π|c_k(f)|\le S_k(f)-s_k(f)$ for the Fourier coefficients $c_k$ is proved in terms of majoring and minoring Riemann sums $S_k(f)$ and $s_f(k)$, respectively, for Riemann integrable functions $f(x)$. This proof has been used in a course on methods of applied mathematics.

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BibTeXRIS

Maurice H. P. M. van Putten. 1997-02-05. A Riemann sum upper bound in the Riemann-Lebesque theorem. https://arxiv.org/abs/funct-an/9702003

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