Abstract
Let (a, b) be a bounded interval and let f be a complex function defined on (a, b). A priori, this function does not have a Fourier series expansion, since this notion has been defined only for functions that are defined and periodic on all of ℝ. However, f can be extended periodically, with period b — a, to all of R as in Figure 6.1.
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© 1999 Springer Science+Business Media New York
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Gasquet, C., Witomski, P. (1999). Expanding a Function in an Orthogonal Basis. In: Fourier Analysis and Applications. Texts in Applied Mathematics, vol 30. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1598-1_6
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DOI: https://doi.org/10.1007/978-1-4612-1598-1_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7211-3
Online ISBN: 978-1-4612-1598-1
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