Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.25930 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911240290304000 |
|---|---|
| author | Semenov, Andrei V. |
| author_facet | Semenov, Andrei V. |
| contents | Let $g \in L^2(\mathbb{R})$ be a rational function of degree $M$, i.e. there exist polynomials $P, Q$ such that $g = {{P} \over {Q}}$ and $deg(P) < deg(Q) \leq M$. We prove that for any $\varepsilon>0$ and any $M \in \mathbb{N}$ there exists universal set $Λ\subset \mathbb{R}$ of density less than $1+\varepsilon$ such that the system $$\left\{ e^{2πi λt } g(t-n) \colon (λ, n) \in Λ\times \mathbb{Z} \right\}$$
is a frame in $L^2(\mathbb{R})$ for any well-behaved rational function $g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25930 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal frame set for rational functions Semenov, Andrei V. Functional Analysis Let $g \in L^2(\mathbb{R})$ be a rational function of degree $M$, i.e. there exist polynomials $P, Q$ such that $g = {{P} \over {Q}}$ and $deg(P) < deg(Q) \leq M$. We prove that for any $\varepsilon>0$ and any $M \in \mathbb{N}$ there exists universal set $Λ\subset \mathbb{R}$ of density less than $1+\varepsilon$ such that the system $$\left\{ e^{2πi λt } g(t-n) \colon (λ, n) \in Λ\times \mathbb{Z} \right\}$$ is a frame in $L^2(\mathbb{R})$ for any well-behaved rational function $g$. |
| title | Universal frame set for rational functions |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2510.25930 |