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A Remark on Fourier Transforms
Mathematical Proceedings of the Cambridge Philosophical Society, 19361. Let f(x) be a complex function belonging to LP (−∞, ∞); i.e. let f(x) be measurable, and |f(x)|p integrable, over (−∞, ∞). The functionis called the Fourier transform of f(x), if the integral on the right exists, in some sense, for almost every value of y. It is well known that, if 1 ≤ p ≤ 2, the integral (1) converges in mean, with index p′ = p/(p –
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Fourier Transforms and Fourier Transforms N.M.R.
2023Gwenola Burgot, Jean-Louis Burgot
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2018
In the previous chapter, we observed a peculiar relation between the smoothness and the rapidity of vanishing at infinity of a function f, as well as its Fourier transform \(\hat {f}\). Based upon this observation, we introduce an important function space \(\mathfrak {S}\), which is invariant under the Fourier transforms. We then proceed to \(\mathfrak
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In the previous chapter, we observed a peculiar relation between the smoothness and the rapidity of vanishing at infinity of a function f, as well as its Fourier transform \(\hat {f}\). Based upon this observation, we introduce an important function space \(\mathfrak {S}\), which is invariant under the Fourier transforms. We then proceed to \(\mathfrak
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Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
, 1977R. Strichartz
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Fourier Transforms in the Complex Domain
, 1934L. S. Basanquet, R. Paley, N. Wiener
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