Geodesic
On the Smoothness of General Kernels
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 443-448

Voir la notice de l'article provenant de la source Cambridge University Press

In (3, §2), the writer and F. E. Browder stated briefly, without proof, some results concerning general distribution kernels. It is our aim here to prove and complete those results.The terminology and notations are introduced in §1.In §2 we define the notion of domain of dependence with respect to the kernel Kx,y (Definition 1) as well as the notion of smoothness of a distribution kernel at a point (Definition 2). Theorem 1 states that the set of points, where the distribution kernel is smooth, is open and the kernel is a smooth function in this set. Theorems 2 and 3 are the converse of Theorem 1. 
Barros-Neto, Jose. On the Smoothness of General Kernels. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 443-448. doi: 10.4153/CJM-1966-047-4
@article{10_4153_CJM_1966_047_4,
     author = {Barros-Neto, Jose},
     title = {On the {Smoothness} of {General} {Kernels}},
     journal = {Canadian journal of mathematics},
     pages = {443--448},
     year = {1966},
     volume = {18},
     number = {1},
     doi = {10.4153/CJM-1966-047-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-047-4/}
}
TY  - JOUR
AU  - Barros-Neto, Jose
TI  - On the Smoothness of General Kernels
JO  - Canadian journal of mathematics
PY  - 1966
SP  - 443
EP  - 448
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-047-4/
DO  - 10.4153/CJM-1966-047-4
ID  - 10_4153_CJM_1966_047_4
ER  - 
%0 Journal Article
%A Barros-Neto, Jose
%T On the Smoothness of General Kernels
%J Canadian journal of mathematics
%D 1966
%P 443-448
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-047-4/
%R 10.4153/CJM-1966-047-4
%F 10_4153_CJM_1966_047_4

[1] 1. Barros-Neto, Jose, Analytic distribution kernels, Trans. Amer. Math. Soc, 100 (1961), 425–438. Google Scholar

[2] 2. Barros-Neto, Jose, Analytic composition kernels on Lie groups, Pacific J. Math., 12 (1962), 661–678. Google Scholar

[3] 3. Barros-Neto, Jose and Browder, Felix E., The analyticity of kernels, Can. J. Math., 18 (1961), 645–649. Google Scholar

[4] 4. Browder, Felix E., Real analytic functions on product spaces and separate analyticity, Can. J. Math., 13(1961), 650–656. Google Scholar

[5] 5. Grothendieck, A., Espaces vectoriels topologiques (S. Paulo, 1954). Google Scholar

[6] 6. Schwartz, L., Théorie des distributions, tome I (Paris, 1950). Google Scholar

[7] 7. Schwartz, L., Equations aux dérivées partielles, Séminaire 1954-55, Institut Henri Poincaré, Paris. Google Scholar

Cité par Sources :