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A Note on Asymptotic Series

Published online by Cambridge University Press:  20 November 2018

Harry F. Davis
Harry F. Davis*
Affiliation:
University of British Columbia
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Extract

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We extend some observations of Popken (2) on the algebraic foundations of the theory of asymptotic series. The main result is the theorem in §5 which characterizes, for a particular function space, a class of linear functionals defined in §4. In §3 we discuss another class of linear functionals related to asymptotic series. In the first two paragraphs we give definitions which render this note self-contained.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 90 - 95
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Borel, E., Leçons sur les séries divergentes (Paris, 1928).Google Scholar
2. Popken, J., Asymptotic expansions from an algebraic standpoint, Nederl. Akad. Wetensch. Proc. Ser. A 56 = Indagationes Math. 15 (1953), 131–143.Google Scholar
3. Widder, D. W., The Laplace Transform (Princeton, 1940).Google Scholar