Ultrafunctions are a particular class of functions defined on a non- Archimedean field R∗⊃RR∗⊃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.
Basic properties of ultrafunctions / V. Benci, L. Luperi Baglini (PROGRESS IN NONLINEAR DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS). - In: Analysis and Topology in Nonlinear Differential Equations : A Tribute to Bernhard Ruf on the Occasion of his 60th Birthday / [a cura di] D.G de Figueiredo, J.M. do Ó, C. Tomei. - Prima edizione. - [s.l] : Springer Nature, 2014. - ISBN 9783319042138. - pp. 61-86 (( Intervento presentato al 9. convegno Workshop on Nonlinear Differential Equations tenutosi a Joao Pessoa nel 2012 [10.1007/978-3-319-04214-5_4].
Basic properties of ultrafunctions
L. Luperi Baglini
2014
Abstract
Ultrafunctions are a particular class of functions defined on a non- Archimedean field R∗⊃RR∗⊃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.
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