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.
Generalized functions beyond distributions / V. Benci, L. Luperi Baglini. - In: ARABIAN JOURNAL OF MATHEMATICS. - ISSN 2193-5343. - 4:4(2015 Dec), pp. 231-253. [10.1007/s40065-014-0114-5]
Generalized functions beyond distributions
L. Luperi Baglini
2015
Abstract
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.
| File | Dimensione | Formato | |
|---|---|---|---|
|
Generalized Functions Beyond Distributions.pdf
accesso aperto
Tipologia:
Publisher's version/PDF
Dimensione
435.26 kB
Formato
Adobe PDF
|
435.26 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
