Abstract
In this chapter, we shall study some basic properties of the Fourier transform. Section 1.1 is concerned with its definition and properties in \(L^1(\mathbb{R}^n)\). The case \(L^2(\mathbb{R}^n)\;\) is considered in Section 1.2. The space of tempered distributions is briefly considered in Section 1.3. Finally, Sections 1.4 and 1.5 give an introduction to the study of oscillatory integrals in one dimension and some applications, respectively.
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© 2015 Springer-Verlag New York
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Linares, F., Ponce, G. (2015). The Fourier Transform. In: Introduction to Nonlinear Dispersive Equations. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2181-2_1
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DOI: https://doi.org/10.1007/978-1-4939-2181-2_1
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2180-5
Online ISBN: 978-1-4939-2181-2
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