Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T04:24:02.553Z Has data issue: false hasContentIssue false

An Inverse Mapping Theorem in Frechet Spaces

Published online by Cambridge University Press:  20 November 2018

Henri-François Gautrin
Affiliation:
Département de Mathématiques Et Statistique, Université de Montréal
Khaldoun Imam
Affiliation:
Département de Mathématiques Et Statistique, Université de Montréal
Tapio Klemola
Affiliation:
Département de Mathématiques Et Statistique, Université de Montréal
Jean-Marc Terrier
Affiliation:
Département de Mathématiques Et Statistique, Université de Montréal
Rights & Permissions [Opens in a new window]

Abstract

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.

Within the framework of a-differentiability, introduced by H. R. Fischer in locally convex spaces, sufficient conditions for an inverse mapping theorem between Fréchet spaces are established.

Resume

Resume

En se basant sur les propriétés de la σ-différentiabilité introduite par H. R. Fischer dans les espaces localement convexes, les auteurs établissent des conditions suffisantes pour obtenir un théorème “d'application inverse” entre deux espaces de Fréchet.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Cartan, H., Cours de calcul différentiel, Hermann, Paris.Google Scholar
2. Fischer, H.R., Differentialrechnung in lokalkonvexen Râumen und Mannigfaltigkeiten von Abbildungen, Manuskript der Fakultàt fur Mathematik und Informatik, Universitàt Mannheim, Mannheim 1977.Google Scholar
3. Hamilton, R.S., The inverse function theorem of Nash and Moser, Bulletin of the American Mathematical Society, Vol. 7 (1982), pp. 65222.Google Scholar
4. Lojasiewicz, S., Inverse function theorem, Zeszyty Naukowe Uniwersytetu Jagiellonskiego, Vol. 441 (1977), pp. 79.Google Scholar
5. Lojasiewicz, S. and Zehnder, E., An inverse function theorem in Fréchet spaces, Journal of Functional Analysis, Vol. 33 (1979), pp. 165174.Google Scholar
6. Omori, H., Infinite dimensional Lie transformation groups, Lectures Notes in Mathematics, 427, Springer Verlag, 1974.Google Scholar
7. Yamamuro, S., Notes on the inverse mapping theorem in locally convex spaces, Bulletin of the Australian Mathematical Society, Vol. 21 (1980), pp. 419461.Google Scholar
8. Yamamuro, S., Differential calculus in topological linear spaces, Lectures Notes in Mathematics, 374, Springer Verlag, 1974.Google Scholar