Work

A Fréchet Lie group on distributions

Year: 2024

Type: article

Abstract: Solving non-autonomous systems of ordinary differential equations leads to consider a new product of bivariate distributions called the ⋆ product in the literature. This product, distinct from the convolution product, has recently been used to establish structural results concerning non-autonomous differential systems, yet its formal underpinnings remain unclear. We demonstrate that it is well-defined on the weak closure of the space of smooth functions on a compact subset of R 2 . We establish that a subset of this weak closure has the structure of a Fréchet space D . The ⋆ product arises from the composition of endomorphisms of that space. Invertible elements of D form a dense subset of it and a Fréchet Lie group for the operation ⋆. This product generalizes the convolution, Volterra compositions of first and second type and induces Schwartz's bracket.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2024.129195

Authors: Manon Ryckebusch, Abderrahman Bouhamidi, Pierre-Louis Giscard

Institution: Université du littoral côte d'opale

Language: English

Topic: Mathematical and Theoretical Analysis

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,100

Funder: Agence Nationale de la Recherche