Distributions - Convolution and Fourier transform : Convolution product of distributions

Convolution product of distributions
Distributions - Convolution and Fourier transform

Author : Michel DOISY

Review date: April 26, 2021 | Lire en français

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2. Convolution product of distributions

If f and g are two functions of $ℝ$ in $ℝ$ , we define their tensor product as the function of two variables :

f Ä g(x, y) = f (x)g(y)

Using Fubini's theorem, we verify that if f and g are locally integrable on $ℝ$ , then f Ä g is also integrable on

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Convolution product of distributions

(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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