Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T06:18:10.829Z Has data issue: false hasContentIssue false
  • English
  • Français

ULTRAMETRIC AND NON-LOCALLY CONVEX ANALOGUES OF THE GENERAL CURVE LEMMA OF CONVENIENT DIFFERENTIAL CALCULUS

Published online by Cambridge University Press:  01 May 2008

HELGE GLÖCKNER
HELGE GLÖCKNER*
Affiliation:
Universität Paderborn, Institut für Mathematik, Warburger Str. 100, 33098 Paderborn, Germany e-mail: [email protected]
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.

The General Curve Lemma is a tool of Infinite-Dimensional Analysis that enables refined studies of differentiability properties of maps between real locally convex spaces to be made. In this article, we generalize the General Curve Lemma in two ways. First, we remove the condition of local convexity in the real case. Second, we adapt the lemma to the case of curves in topological vector spaces over ultrametric fields.

Keywords

26E1526E2026E3045T2046A1646S10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 2 , May 2008 , pp. 271 - 288
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Adasch, N., Ernst, B. and Keim, D., Topological vector spaces. The theory without convexity conditions, (Springer-Verlag, 1978).Google Scholar
2.Bertram, W., Differential geometry, Lie groups and symmetric spaces over general base fields and rings, Memoirs of the AMS 192 (2008), no. 900, 186+v pp.CrossRefGoogle Scholar
3.Bertram, W., Glöckner, H. and Neeb, K.-H., Differential calculus over general base fields and rings, Expo. Math. 22 (2004), 213–282.CrossRefGoogle Scholar
4.Boman, J.Differentiability of a function and of its compositions with functions of one variable, Math Scand. 20 (1967), 249–268.CrossRefGoogle Scholar
5.Bourbaki, N.Topological vector spaces Chapters 1–5, (Springer-Verlag, 1987).CrossRefGoogle Scholar
6.De Smedt, S.p-adic continuously differentiable functions of several variables, Collect. Math. 45 (1994), 137–152.Google Scholar
7.Frölicher, A., and Kriegl, A.Linear spaces and differentiation theory, (John Wiley, 1988).Google Scholar
8.Glöckner, H.Smooth Lie groups over local fields of positive characteristic need not be analytic, J. Algebra 285 (2005), 356–371.CrossRefGoogle Scholar
9.Glöckner, H.Every smooth p-adic Lie group admits a compatible analytic structure, Forum Math. 18 (2006), 45–84.CrossRefGoogle Scholar
10.Glöckner, H., Aspects of p-adic non-linear functional analysis, Khrennikov, A. Yu., Rakić, Z. and Volovich, I. V. (Eds.), p-Adic Mathematical Physics. 2nd International Conference (Belgrade, 2005), AIP Conference Proceedings 826, (Amer. Inst. Physics, New York, 2006) (cf. arXiv:math/0602081), 237–253.Google Scholar
11.Glöckner, H.Comparison of some notions of Ck-maps in multi-variable non-archimedian analysis, Bull. Belg. Math. Soc. Simon Stevin 14 (2007), 877–904.CrossRefGoogle Scholar
12.Glöckner, H., Lie groups over non-discrete topological fields, preprint, arXiv:math/0408008.Google Scholar
13.Glöckner, H., Finite order differentiability properties, fixed points and implicit functions over valued fields, preprint, arXiv:math/0511218.Google Scholar
14.Glöckner, H., and Neeb, K.-H., Infinite-dimensional Lie groups, Vol. I; book in preparation.Google Scholar
15.Jarchow, H.Locally convex spaces, (B. G. Teubner, Stuttgart, 1981).CrossRefGoogle Scholar
16.Kalton, N. J., Peck, N. T. and Roberts, J. W.An F-space sampler, (Cambridge University Press, 1984).CrossRefGoogle Scholar
17.Kriegl, A., and Michor, P. W., The convenient setting of global analysis, Amer. Math. Soc., (Providence, 1997).Google Scholar
18.Ludkovsky, S. V.Irreducible unitary representations of non-Archimedean groups of diffeomorphisms, Southeast Asian Bull. Math. 22 (1998), 419–436.Google Scholar
19.Ludkovsky, S. V.Quasi-invariant measures on non-Archimedean groups and semigroups of loops and paths, their representations I, II Ann. Math. Blaise Pascal 7 (2000), 19–53 and 55–80.CrossRefGoogle Scholar
20.Ludkovsky, S. V., Smoothness of functions global and along curves over ultra-metric fields, arXiv:math/0608725.Google Scholar
21.Schikhof, W. H.Ultrametric calculus, (Cambridge University Press, 1984).Google Scholar