Abstract
Fourier series and their ilk are designed to solve boundary value problems on bounded intervals. The extension of the Fourier calculus to the entire real line leads naturally to the Fourier transform, a powerful mathematical tool for the analysis of aperiodic functions. The Fourier transform is of fundamental importance in a remarkably broad range of applications, including both ordinary and partial differential equations, probability, quantum mechanics, signal and image processing, and control theory, to name but a few.
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© 2014 Springer International Publishing Switzerland
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Olver, P.J. (2014). Fourier Transforms. In: Introduction to Partial Differential Equations. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-02099-0_7
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DOI: https://doi.org/10.1007/978-3-319-02099-0_7
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-02098-3
Online ISBN: 978-3-319-02099-0
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