Hostname: page-component-cb9f654ff-9b74x Total loading time: 0 Render date: 2025-08-21T10:46:34.591Z Has data issue: false hasContentIssue false
  • English
  • Français

Derivatives of vector-valued functions

Published online by Cambridge University Press:  26 February 2010

R. E. Edwards
R. E. Edwards
Affiliation:
Birkbeck College, London.
Get access

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1.Grothendieck, A., “Sur certains espaces de functions holomorphes I”, Journal reine angew. Math., 192 (1) (1953), 35‖64.CrossRefGoogle Scholar
2.Hille, E., “Functional analysis and semigroups”, Amer. Math. Soc. Coll. Pubs., XXXI (New York, 1948).Google Scholar
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