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Arabian Journal of Mathematics

, Volume 4, Issue 4, pp 231–253 | Cite as

Generalized functions beyond distributions

  • Vieri BenciEmail author
  • Lorenzo Luperi Baglini
Open Access
Article

Abstract

Ultrafunctions are a particular class of functions defined on a non-Archimedean field \({\mathbb{R}^{\ast } \supset \mathbb{R}}\). They have been introduced and studied in some previous works (Benci, Adv Nonlinear Stud 13:461–486, 2013; Benci and Luperi Baglini, EJDE, Conf 21:11–21, 2014; Benci, Basic Properties of ultrafunctions, to appear in the WNDE2012 Conference Proceedings, arXiv:1302.7156, 2014). In this paper we introduce a modified notion of ultrafunction and discuss systematically the properties that this modification allows. In particular, we will concentrate on the definition and the properties of the operators of derivation and integration of ultrafunctions.

Mathematics Subject Classification

26E30 26E35 46F30 

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Copyright information

© The Author(s) 2014

Open AccessThis article is distributed under the terms of the Creative CommonsAttribution License which permits any use, Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di PisaPisaItaly
  2. 2.Department of Mathematics, College of ScienceKing Saud UniversityRiyadhSaudi Arabia
  3. 3.Faculty of MathematicsUniversity of ViennaViennaAustria

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