Distributions - Convolution and Fourier transform : Distribution support

Distribution support
Distributions - Convolution and Fourier transform

Author : Michel DOISY

Review date: April 26, 2021 | Lire en français

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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: $Supp (f) = \bar{{x \in ℝ / f (x) \neq 0}}$

where the bar...

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Convolution product of distributions

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).
(3) - SAICHEV...

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Distribution support Distributions - Convolution and Fourier transform

1. Distribution support

References

Distribution support
Distributions - Convolution and Fourier transform