On polynomial $d$-chaos via $d$-dissociated character subsystems on compact abelian groups
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911640621940736 |
|---|---|
| author | Kazakova, Anna |
| author_facet | Kazakova, Anna |
| contents | In this paper, we study polynomial chaoses of degree $d$ constructed from sequences of functions; that is, sets of all possible $d$-fold products of sequence elements, allowing repeated factors. The tetrahedral chaos of degree $d$ is defined as the subset consisting of products with pairwise distinct factors. We prove that polynomial $d$-chaoses (and, consequently, the tetrahedral chaoses) with respect to $d$-dissociated subsystems of characters on compact abelian groups are $q$-lacunary and $2d/(d+1)$-Sidon systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01572 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On polynomial $d$-chaos via $d$-dissociated character subsystems on compact abelian groups Kazakova, Anna Functional Analysis Dynamical Systems In this paper, we study polynomial chaoses of degree $d$ constructed from sequences of functions; that is, sets of all possible $d$-fold products of sequence elements, allowing repeated factors. The tetrahedral chaos of degree $d$ is defined as the subset consisting of products with pairwise distinct factors. We prove that polynomial $d$-chaoses (and, consequently, the tetrahedral chaoses) with respect to $d$-dissociated subsystems of characters on compact abelian groups are $q$-lacunary and $2d/(d+1)$-Sidon systems. |
| title | On polynomial $d$-chaos via $d$-dissociated character subsystems on compact abelian groups |
| topic | Functional Analysis Dynamical Systems |
| url | https://arxiv.org/abs/2605.01572 |