Integrable functions for the Bernoulli measures of rank $1$

Maïga, Hamadoun

doi:10.5802/ambp.287

Integrable functions for the Bernoulli measures of rank

1

Maïga, Hamadoun ¹

¹ Département de Mathématiques et d’Informatique Faculté des Sciences et Techniques Université de Bamako Bamako Mali

Annales mathématiques Blaise Pascal, Tome 17 (2010) no. 2, pp. 341-356

Résumé

In this paper, following the $p$ -adic integration theory worked out by A. F. Monna and T. A. Springer [4, 5] and generalized by A. C. M. van Rooij and W. H. Schikhof [6, 7] for the spaces which are not $σ$ -compacts, we study the class of integrable $p$ -adic functions with respect to Bernoulli measures of rank $1$ . Among these measures, we characterize those which are invertible and we give their inverse in the form of series.

MR Zbl

DOI : 10.5802/ambp.287

Classification : 46S10
Keywords: integrable functions, Bernoulli measures of rank $1$, invertible measures

Affiliations des auteurs :

Maïga, Hamadoun ¹

¹ Département de Mathématiques et d’Informatique Faculté des Sciences et Techniques Université de Bamako Bamako Mali

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Maïga, Hamadoun. Integrable functions for the Bernoulli measures of rank $1$. Annales mathématiques Blaise Pascal, Tome 17 (2010) no. 2, pp. 341-356. doi: 10.5802/ambp.287

Bibliographie
Cité par

[1] Diarra, Bertin Base de Mahler et autres, Séminaire d’Analyse, 1994–1995 (Aubière) (Sémin. Anal. Univ. Blaise Pascal (Clermont II)), Volume 10, Univ. Blaise Pascal (Clermont II), Clermont-Ferrand, 1997, pp. Exp. No. 16, 18 | Zbl | MR

[2] Diarra, Bertin Cours d’analyse $p$ -adique (1999 - 2000) (Technical report http://math.univ-bpclermont.fr/ diarra)

[3] Koblitz, Neal $p$ -adic Numbers, $p$ -adic Analysis and Zeta-Functions, Springer-Verlag, New York - Heidelberg - Berlin, 1977 | Zbl | MR

[4] Monna, A. F.; Springer, T. A. Intégration non-archimédienne. I, Nederl. Akad. Wetensch. Proc. Ser. A 66=Indag. Math., Volume 25 (1963), pp. 634-642 | Zbl | MR

[5] Monna, A. F.; Springer, T. A. Intégration non-archimédienne. II, Nederl. Akad. Wetensch. Proc. Ser. A 66=Indag. Math., Volume 25 (1963), pp. 643-653 | Zbl | MR

[6] van Rooij, Arnoud C. M. Non-Archimedean Functional Analysis, M. Dekker, New York and Basel, 1978 | Zbl | MR

[7] Schikhof, Wilhelmus H. Ultrametric calculus - An introduction to p-adic analysis, Cambridge University Press, Cambridge, 1984 | Zbl | MR

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