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Nuclear Spaces of Generalized Test Functions

Published online by Cambridge University Press:  20 November 2018

H. Millington
H. Millington*
Affiliation:
University of British Columbia, Vancouver, British Columbia
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It is well known that a large proportion of the locally convex spaces encountered in distribution theory are nuclear (Grothendieck [4], Treves [10], Schaeffer [8].) In [1] Beurling introduced spaces of test functions more general than those previously used. In this paper we shall show that many of these spaces, and resulting spaces of distributions, are also nuclear spaces.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 2 , June 1973 , pp. 269 - 273
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Beurling, A., Quasi-analyticity and general distributions, Lectures 4 and 5, (mimeographed). Amer. Math. Soc. Summer Inst., Stanford, 1961.Google Scholar
2. Björck, G., Linear partial differential operators and generalized distributions, Ark. Mat. 6 (1965–67), 352–407.Google Scholar
3. Gelfand, I. M. and Vilenkin, N. Y., Generalized functions, Vol 4, Academic Press, New York, 1964.Google Scholar
4. Grothendieck, A., Produits tensoriels topologiques et espaces nucléaires, Memoirs Amer. Math. Soc. 16, 1955.Google Scholar
5. Pietsch, A., Eine neue Characterisierung der nukleare lokalkonvexen Ràume, Math. Nachr. 25 (1963), 31–36.Google Scholar
6. Robertson, A. P. and Roberton, W. J., Topological vector spaces, Cambridge Univ. Press, New York, 1966.Google Scholar
7. Rudin, W., Fourier analysis on groups, Interscience, New York, 1962.Google Scholar
8. Schaeffer, H., Topological vector spaces, Macmillan, New York, 1966.Google Scholar
9. Sion, M., An introduction to real analysis, Holt, New York, 1968.Google Scholar
10. Treves, F., Topological vector spaces, Distributions and Kernels. Academic Press, New York, 1967.Google Scholar