Integrable functions for the Bernoulli measures of rank 1

Hamadoun Maïga[1]

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

Annales mathématiques Blaise Pascal (2010)

  • Volume: 17, Issue: 2, page 341-356
  • ISSN: 1259-1734

Abstract

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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.

How to cite

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Maïga, Hamadoun. "Integrable functions for the Bernoulli measures of rank $1$." Annales mathématiques Blaise Pascal 17.2 (2010): 341-356. <http://eudml.org/doc/116356>.

@article{Maïga2010,
abstract = {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 $\sigma $-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.},
affiliation = {Département de Mathématiques et d’Informatique Faculté des Sciences et Techniques Université de Bamako Bamako Mali},
author = {Maïga, Hamadoun},
journal = {Annales mathématiques Blaise Pascal},
keywords = {integrable functions; Bernoulli measures of rank $1$; invertible measures; Bernoulli measures of rank 1},
language = {eng},
month = {7},
number = {2},
pages = {341-356},
publisher = {Annales mathématiques Blaise Pascal},
title = {Integrable functions for the Bernoulli measures of rank $1$},
url = {http://eudml.org/doc/116356},
volume = {17},
year = {2010},
}

TY - JOUR
AU - Maïga, Hamadoun
TI - Integrable functions for the Bernoulli measures of rank $1$
JO - Annales mathématiques Blaise Pascal
DA - 2010/7//
PB - Annales mathématiques Blaise Pascal
VL - 17
IS - 2
SP - 341
EP - 356
AB - 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 $\sigma $-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.
LA - eng
KW - integrable functions; Bernoulli measures of rank $1$; invertible measures; Bernoulli measures of rank 1
UR - http://eudml.org/doc/116356
ER -

References

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  1. Bertin Diarra, Base de Mahler et autres, Séminaire d’Analyse, 1994–1995 (Aubière) 10 (1997), Univ. Blaise Pascal (Clermont II), Clermont-Ferrand Zbl0999.12014MR1461327
  2. Bertin Diarra, Cours d’analyse p -adique, (1999 - 2000) Zbl0633.12008
  3. Neal Koblitz, p -adic Numbers, p -adic Analysis and Zeta-Functions, (1977), Springer-Verlag, New York - Heidelberg - Berlin Zbl0364.12015MR466081
  4. A. F. Monna, T. A. Springer, Intégration non-archimédienne. I, Nederl. Akad. Wetensch. Proc. Ser. A 66=Indag. Math. 25 (1963), 634-642 Zbl0147.11803MR156936
  5. A. F. Monna, T. A. Springer, Intégration non-archimédienne. II, Nederl. Akad. Wetensch. Proc. Ser. A 66=Indag. Math. 25 (1963), 643-653 Zbl0147.11803MR156937
  6. Arnoud C. M. van Rooij, Non-Archimedean Functional Analysis, (1978), M. Dekker, New York and Basel Zbl0396.46061MR512894
  7. Wilhelmus H. Schikhof, Ultrametric calculus - An introduction to p-adic analysis, (1984), Cambridge University Press, Cambridge Zbl0553.26006MR791759

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