Fourier Series

Steen Pedersen ()
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Steen Pedersen: Wright State University, Department of Mathematics

Chapter 12 in From Calculus to Analysis, 2015, pp 247-279 from Springer

Abstract: Abstract Our approach to Fourier series is based on some rudimentary facts about linear spaces equipped with an inner product. Our approach to pointwise convergence is based on Dini’s criterion. We discuss uniform convergence and Cesàro summability of Fourier series. We also show the Fourier series of a Riemann integrable function convergences in the mean. We establish Weyl’s criterion for uniform distribution of sequences. As an application, we establish the uniform distribution in the unit interval of the fractional parts of the integer multiples of an irrational number.

Keywords: Fourier Series; Integrable Function; Fourier Coefficient; Pointwise Convergence; Irrational Number (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-13641-7_12

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DOI: 10.1007/978-3-319-13641-7_12

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