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Derivatives of vector-valued functions

Published online by Cambridge University Press:  26 February 2010

R. E. Edwards
R. E. Edwards
Affiliation:
Birkbeck College, London.
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Extract

In all that follows, E denotes a separated locally convex space, E' its topological dual, and <x, x−> the bilinear form expressing the duality. We consider the differentiation of a function f:t → f(t) of a real variable t which takes its value in E; the domain of f will be an open interval which, without loss of generality, may be taken to be the entire real axis. There are various senses in which the derivative may or may not exist, and it is proposed to consider some relations between these senses.

Type
Research Article
Information
Mathematika , Volume 5 , Issue 1 , June 1958 , pp. 58 - 61
Copyright
Copyright © University College London 1958

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References

1.Grothendieck, A., “Sur certains espaces de functions holomorphes I”, Journal reine angew. Math., 192 (1) (1953), 35‖64.CrossRefGoogle Scholar
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3.Schwartz, L., “Un lemme sur la derivation des fonetions vectorielles d'une variable reelle,” Annales Inst. Fourier, II (1950), 17–18.CrossRefGoogle Scholar
4.Bourbaki, N., Eléments de Mathdmatique, Espaces Vectoriels Topologiques, Oh. III–V, Act. Sci. et Ind., No. 1229, Paris (1955).Google Scholar