2014/01/21 by Vieri Benci, Benci, Vieri, Lorenzo Luperi Baglini +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #advanced mathematical theories #math.FA
paper · pdf · doi:10.48550/arxiv.1401.5270
29 pages, Keywords: Ultrafunctions, Delta function, distributions, Non Archimedean Mathematics, Non Standard Analysis. arXiv admin note: text overlap with arXiv:1302.7156
arxiv created 2014/01/21 · openalex publication_date 2014/01/21 · arxiv updated 2014/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ([1],[2],[3]). In this paper we introduce a modified notion of ultrafunction and we discuss sistematically the properties that this modification allows. In particular, we will concentrated on the definition and the properties of the operators of derivation and integration of ultrafunctions.