A Riemann sum upper bound in the Riemann-Lebesque theorem
Abstract
The Riemann-Lebesque Theorem is commonly proved in a few strokes using the theory of Lebesque integration. Here, the upper bound 2π|ck(f)| Sk(f)-sk(f) for the Fourier coefficients ck is proved in terms of majoring and minoring Riemann sums Sk(f) and sf(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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