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The Analyticity of Kernels

Published online by Cambridge University Press:  20 November 2018

J. De Barros-Neto  and
F. E. Browder
J. De Barros-Neto
Affiliation:
Instituto de Matematica Pure e Aplicada Rio de Janeiro
F. E. Browder
Affiliation:
Yale University
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Let V be a paracompact real analytic manifold of dimension n ≥ 1. Following the terminology of the theory of distributions of Schwartz (4), is the linear space of infinitely differentiable functions with compact support in V with the appropriate inductive limit topology, is the Frechet space of infinitely differentiable functions on V, is the dual space of consisting of the distributions on V, the dual space of consisting of the distributions with compact support on V. Let 𝒰(V) be the linear space of real analytic functions on V.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 645 - 649
Copyright
Copyright © Canadian Mathematical Society 1961

References

1. de Barros-Neto, J., Thesis (University of Sâo Paulo, 1960).Google Scholar
2. Browder, F. E., Real analytic functions on product spaces and separate analyticity, Can. J. Math., 13 (1961), 650–656.Google Scholar
3. Grothendieck, A., Espaces vectoriels topologiques (Sao Paulo, 1954).Google Scholar
4. Schwartz, L., Théorie des distributions (Paris, 1950-1).Google Scholar
5. Schwartz, L., Théorie des noyaux, Cambridge International Mathematical Congress (1950).Google Scholar