Abstract
We have seen in the last few lessons how it is necessary to restrict the choice of functions in L 1(ℝ) if we wish to use the differentiation formulas and define the inverse Fourier transform. In this lesson, we are going to introduce a subspace of L 1(ℝ) that is invariant under the Fourier transform, differentiation, and multiplication by polynomials.
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© 1999 Springer Science+Business Media New York
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Gasquet, C., Witomski, P. (1999). The Space ℒ (ℝ). 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_19
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DOI: https://doi.org/10.1007/978-1-4612-1598-1_19
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7211-3
Online ISBN: 978-1-4612-1598-1
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