Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-05-18T13:42:35.048Z Has data issue: false hasContentIssue false
  • English
  • Français

On Conditions of Differentiability of Locally Compact Groups

Published online by Cambridge University Press:  22 January 2016

Masatake Kuranishi
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A formulation of the differentiability of the product function of a locally compact group at the identity may be given in the following way: In a sufficiently small euclidean neighborhood of the identity product satisfies the condition:

where M(λ) is a function such that M(λ) → 0 as λ → 0, From this we can deduce easily

.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 1 , June 1950 , pp. 71 - 81
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1950

References

[1] Birkhoff, Garret, Analytical groups, Trans. Am. Math. Soc. Vol. 43 (1943). 61–101.CrossRefGoogle Scholar
[2] Gleason, A., On the structure of locally compact groups, Proc. of Nat. Acad. Vol. 35 (1949), pp. 384–386.CrossRefGoogle ScholarPubMed
[3] Iwasawa, K., On some types of topological groups, Ann. of Math. Vol. 50 (1949), pp. 507–558.CrossRefGoogle Scholar
[4] Kuranishi, M., On euclidean local groups satisfying certain conditions, to appear in Bull. Amer. Math. Soc. Google Scholar
[5] Montgomery, D., Topological groups of differentiable transformations, Ann. of Math., Vol. 46 (1945), pp. 382–387.Google Scholar
[6] Montgomery, D., Locally compact groups of differentiate transformations, Ann. of Math., Vol, 47 (1946), pp. 639–653.Google Scholar
[7] Montgomery, D., Connected one-dimensional group, Ann. of Math. Vol. 49 (1948), pp. 110–117.Google Scholar
[8] Pontrjagin, L., Topological groups, 1936, Princeton.Google Scholar
[9] Smith, P., Foundations of the theory of Lie groups with real parameter. Ann. of Math. Vol. 44 (1943), pp. 481–513.Google Scholar
[10] Weil, A., Sur les espaces à structure uniform et sur la topologie générale, Actualities Scien. et Industrielles 55, 1938. Hermann, Paris.Google Scholar