1. Distribution support

This is an important notion, particularly for the definition of the convolution product of distributions.

Recall that if f is a function of $ℝ$ in $ℂ$ , its support is the complementary of the largest open on which it cancels. Or again: $Supp (f) = \overset{}{{x \in ℝ / f (x) \neq 0}}$

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Distribution support

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page Distributions - Convolution and Fourier transform

Convolution product of distributions

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References

(1) - GASQUET (C.), WITOMSKI (P.) - Analyse de Fourier et applications. Filtrage – Calcul Numérique – Ondelettes - . 354 p. – Masson – Paris (1990).
(2) - HERVÉ (M.) - Transformation de Fourier et distributions - . 182 p. – PUF – Paris (1986).

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