An Integro-Differential Structure for Dirac Distributions
Rings and Algebras
2023-08-11 v3 Classical Analysis and ODEs
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.
Cite
@article{arxiv.1707.06591,
title = {An Integro-Differential Structure for Dirac Distributions},
author = {Markus Rosenkranz and Nitin Serwa},
journal= {arXiv preprint arXiv:1707.06591},
year = {2023}
}
Comments
38 pages