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Fourier Series

In: From Calculus to Analysis

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  • Steen Pedersen

    (Wright State University, Department of Mathematics)

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.

Suggested Citation

  • Steen Pedersen, 2015. "Fourier Series," Springer Books, in: From Calculus to Analysis, edition 127, chapter 12, pages 247-279, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-13641-7_12
    DOI: 10.1007/978-3-319-13641-7_12
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