Topology and geometry of the general composition of formal power series -- towards Fréchet-Lie group-like formalism
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916884506476544 |
|---|---|
| author | Bugajewski, Dawid |
| author_facet | Bugajewski, Dawid |
| contents | 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 Fréchet 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 Fréchet-Lie group structures on the set of nonunit formal power series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09853 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topology and geometry of the general composition of formal power series -- towards Fréchet-Lie group-like formalism Bugajewski, Dawid Rings and Algebras Primary: 13F25, Secondary: 13J05, 47H30, 58B10, 22E66, 17B65 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 Fréchet 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 Fréchet-Lie group structures on the set of nonunit formal power series. |
| title | Topology and geometry of the general composition of formal power series -- towards Fréchet-Lie group-like formalism |
| topic | Rings and Algebras Primary: 13F25, Secondary: 13J05, 47H30, 58B10, 22E66, 17B65 |
| url | https://arxiv.org/abs/2409.09853 |