Topology and geometry of the general composition of formal power series - towards Fr\'echet-Lie group-like formalism

Autor:	Bugajewski, Dawid
Rok vydání:	2024
Předmět:	Mathematics - Rings and Algebras Primary: 13F25 Secondary: 13J05 47H30 58B10 22E66 17B65
Druh dokumentu:	Working Paper
Popis:	In this article, we study the properties of the autonomous superposition operator on the space of formal power series, including those with nonzero constant term. We prove its continuity and smoothness with respect to the topology of pointwise convergence and a natural Fr\'echet manifold structure. A necessary and sufficient condition for the left composition inverse of a formal power series to exist is provided. We also present some properties of the Fr\'echet-Lie group structures on the set of nonunit formal power series. Comment: 11 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.09853 Zobrazit plný text záznamu View this record from Arxiv