Abstract
In this chapter we study the problem of representing a given T-periodic function as a superposition, for a suitable choice of the coefficients, of more “elementary” ones. This problem was first studied by J. Fourier in the case when the elementary functions are the trigonometric ones (nowadays we know that many different choices are indeed possible). Thanks to the theory of L2 spaces and of Hilbert spaces developed in the previous chapters, the problem can be formalized by looking for complete orthonormal systems in L2 made by trigonometric functions.
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© 2011 Scuola Normale Superiore Pisa
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Ambrosio, L., Da Prato, G., Mennucci, A. (2011). Fourier series. In: Introduction to Measure Theory and Integration. Appunti/Lecture Notes, vol 10. Edizioni della Normale. https://doi.org/10.1007/978-88-7642-386-4_5
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DOI: https://doi.org/10.1007/978-88-7642-386-4_5
Publisher Name: Edizioni della Normale
Print ISBN: 978-88-7642-385-7
Online ISBN: 978-88-7642-386-4
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