no. 1
Some remarks on convolution equations
Annales de l'Institut Fourier, Tome 23 (1973) no. 1, pp. 55-73.

Par voie d’une description de la topologie des espaces E ′ (Ω) (Ω ouvert convexe dans R n ) via la transformation de Fourier, c’est-à-dire leurs structures analytiques uniformes, on arrive à une formule qui décrit l’enveloppe convexe du support singulier d’une distribution T, T∈E ′ . On donne des applications à une classe des distributions qui satisfont à l’égalité

cv.sing.supp.S*T=cv.sing.supp.S+cv.sing.supp.T

pour toutes S∈E ′ .

Using a description of the topology of the spaces E ′ (Ω) (Ω open convex subset of R n ) via the Fourier transform, namely their analytically uniform structures, we arrive at a formula describing the convex hull of the singular support of a distribution T, T∈E ′ . We give applications to a class of distributions T satisfying

cv.sing.supp.S*T=cv.sing.supp.S+cv.sing.supp.T

for all S∈E ′ .

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     title = {Some remarks on convolution equations},
     journal = {Annales de l'Institut Fourier},
     pages = {55--73},
     publisher = {Institut Fourier},
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Berenstein, C. A.; Dostal, M. A. Some remarks on convolution equations. Annales de l'Institut Fourier, Tome 23 (1973) no. 1, pp. 55-73. doi : 10.5802/aif.444. https://aif.centre-mersenne.org/articles/10.5802/aif.444/

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