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The equation y′ = fy in zero residue characteristic

Published online by Cambridge University Press:  18 May 2009

Alain Escassut  and
Marie-Claude Sarmant
Alain Escassut
Affiliation:
Université Blaise Pascal, (Clermont II), Mathematiques pures, F-63177 Aubiere Cedex, France
Marie-Claude Sarmant
Affiliation:
Université Pierre et Marie Curie, Mathematiques, F-75230 Paris 05, France
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Let K be an algebraically closed field complete with respect to an ultrametric absolute value |.| and let k be its residue class field. We assume k to have characteristic zero (hence K has characteristic zero too).

Let D be a clopen bounded infraconnected set [3] in K, let R(D) be the algebra of the rational functions with no pole in D, let ‖.‖D be the norm of uniform convergence on D defined on R(D), and let H(D) be the algebra of the analytic elements on D i.e. the completion of R(D) for the norm ‖.‖D.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 2 , May 1991 , pp. 149 - 153
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

REFERENCES

1.Amice, Y., Les nombres p-adiques, P.U.F. (Paris, 1975).Google Scholar
2.Dwork, B., Lectures on p-adic differential equations (Springer-Verlag, 1982).CrossRefGoogle Scholar
3.Escassut, A., Algèbres de Krasner, Comptes Rendus Acad. Sci. Paris, 272 (1971), 598–601.Google Scholar
4.Escassut, A., Algèbres d'é1éments analytiques en analyse non archimèdienne, Indagationes Math. 36 (1974), 339–351.CrossRefGoogle Scholar
5.Escassut, A., Eléments analytiques et filtres percés sur un ensemble infraconnexe, Annali di Mat. Pura et Appl. Bologna, 110 (1976), 335–352.CrossRefGoogle Scholar
6.Escassut, A., T-filtres, ensembles analytiques et transformation de Fourier p-adique, Ann. Inst. Fourier, 25 (1975), 45–80.CrossRefGoogle Scholar
7.Escassut, A., Algèbres de Krasner intègres et noethériennes, Proc. Koninklijke Neder. Akad. van Wetenschappen, Series A 78 (1976), 109–130.Google Scholar
8.Escassut, A., Derivative of analytic elements on infraconnected clopen sets. Proc. Koninklijke Neder. Akad. van Wetenschappen, Series A 92 (1989), 63–70.Google Scholar
9.Escassut, A. and Sarmant, M. C., The differential equation y′ = fy in the algebras H(D), Collectanea Math. 39 (1988) 31–40.Google Scholar
10.Escassut, A. and Diarra, B., Non constant analytic element with a null derivative on an infraconnected open set. J. London Math. Soc., to appear.Google Scholar
11.Escassut, A., The equation y′ = fy in Cp when f is not quasi-invertible, Revista di Mat. Pura ed Applicata, to appear.Google Scholar
12.Garandel, G., Les semi-normes multiplicatives sur les algèbres d'é1éments analytiques au sens de Krasner, Indagationes Math. 37 (1975), 327–341.CrossRefGoogle Scholar
13.Krasner, M., Prolongement analytique dans les corps valués complets: préservation de l'analycité par la convergence uniforme et par la dérivation; théorème de Mittag-Leffler généralisé pour les éléments analytiques, Comptes Rendus Acad. Sci. Paris 244 (1957), 2570–2573.Google Scholar
14.Krasner, M., Prolongement analytique uniforme et multiforme dans le corps valués complets. Les tendances géométriques en algèbre et théorie des nombres, Colloques Internationaux du C.N.R.S. Paris, 143, C.N.R.S. Paris, 97–141.Google Scholar
15.Robba, Ph., Fonctions analytiques sur les corps valués ultramétriques complets, Prolongement analytique et algèbres de Banach ultramétriques, Astérisque, 10 (1973), 109–220.Google Scholar
16.Sarmant, M. C. and Escassut, A., T-suites idempotentes, Bull. Sci. Math. 106 (1982), 189–203.Google Scholar