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Basic Properties of Ultrafunctions

  • Vieri BenciEmail author
  • Lorenzo Luperi Baglini
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 85)

Abstract

Ultrafunctions are a particular class of functions defined on a non- Archimedean field \( \mathbb{R}^{*} \supset \mathbb{R} \). They provide generalized solutions to functional equations which do not have any solutions among the real functions or the distributions. In this paper we analyze systematically some basic properties of the spaces of ultrafunctions.

Keywords

Ultrafunctions delta function distributions non-Archimedean mathematics non-standard analysis. 

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References

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di PisaPisaItaly
  2. 2.Department of Mathematics College of ScienceKing Saud UniversityRiyadhSaudi Arabia

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