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Classical Fourier Analysis pp 173–240Cite as

Fourier Series

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Part of the book series: Graduate Texts in Mathematics ((GTM,volume 249))

Abstract

Principles of Fourier series go back to ancient times. The attempts of the Pythagorean school to explain musical harmony in terms of whole numbers embrace early elements of a trigonometric nature. The theory of epicycles in the Almagest of Ptolemy, based on work related to the circles of Appolonius, contains ideas of astronomical periodicities that we would interpret today as harmonic analysis. Early studies of acoustical and optical phenomena, as well as periodic astronomical and geophysical occurrences, provided a stimulus in the physical sciences toward the rigorous study of expansions of periodic functions. This study is carefully pursued in this chapter.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, USA

    Loukas Grafakos

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  1. Loukas Grafakos
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Grafakos, L. (2014). Fourier Series. In: Classical Fourier Analysis. Graduate Texts in Mathematics, vol 249. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1194-3_3

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