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

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, TE . 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 SE .

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, TE . 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 SE .

@article{AIF_1973__23_1_55_0,
     author = {Berenstein, C. A. and Dostal, M. A.},
     title = {Some remarks on convolution equations},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {23},
     number = {1},
     year = {1973},
     pages = {55-73},
     doi = {10.5802/aif.444},
     zbl = {0241.46039},
     mrnumber = {49 \#5822},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1973__23_1_55_0}
}
Berenstein, C. A.; Dostal, M. A. Some remarks on convolution equations. Annales de l'Institut Fourier, Volume 23 (1973) no. 1, pp. 55-73. doi : 10.5802/aif.444. http://www.numdam.org/item/AIF_1973__23_1_55_0/

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