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On the Smoothness of General Kernels

Published online by Cambridge University Press:  20 November 2018

Jose Barros-Neto
Jose Barros-Neto*
Affiliation:
Université de Montréal and The University of Rochester
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 443 - 448
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Barros-Neto, Jose, Analytic distribution kernels, Trans. Amer. Math. Soc, 100 (1961), 425–438.Google Scholar
2. Barros-Neto, Jose, Analytic composition kernels on Lie groups, Pacific J. Math., 12 (1962), 661–678.Google Scholar
3. Barros-Neto, Jose and Browder, Felix E., The analyticity of kernels, Can. J. Math., 18 (1961), 645–649.Google Scholar
4. Browder, Felix E., Real analytic functions on product spaces and separate analyticity, Can. J. Math., 13(1961), 650–656.Google Scholar
5. Grothendieck, A., Espaces vectoriels topologiques (S. Paulo, 1954).Google Scholar
6. Schwartz, L., Théorie des distributions, tome I (Paris, 1950).Google Scholar
7. Schwartz, L., Equations aux dérivées partielles, Séminaire 1954-55, Institut Henri Poincaré, Paris.Google Scholar