An integro-differential structure for Dirac distributions. (May 2019)

• Record Type: Journal Article
• Authors: Rosenkranz, Markus; Serwa, Nitin
• Is Part Of: Journal of symbolic computation. Volume 92(2019)
• Page Start: 156
• Page End: 189
• Publication Date: 2019-05
• Subjects: Differential algebra -- Rota–Baxter algebra -- Distribution theory -- Boundary problems; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2018.01.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We develop a new algebraic setting for treating piecewise functions and distributions together with suitable differential and Rota–Baxter structures. Our treatment aims to provide the algebraic underpinning for symbolic computation systems handling such objects. In particular, we show that the Green's function of regular boundary problems (for linear ordinary differential equations) can be expressed naturally in the new setting and that it is characterized by the corresponding distributional differential equation known from analysis.