Generalized functions beyond distributions
- Benci, Vieri (Dipartimento di Matematica, Università degli Studi di Pisa)
- Luperi Baglini, Lorenzo (Faculty of Mathematics, Faculty of Mathematics, University of Vienna)
Publication date
January 2014
DOI Publisher
Springer Science and Business Media LLC Journal
2193-5343Abstract
Ultrafunctions are a particular class of functions defined on a non-Archimedean field R∗⊃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
Add to ORKG