Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2508.15159 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914027013144576 |
|---|---|
| author | Ramabadran, Aditya van Vliet, Johannes |
| author_facet | Ramabadran, Aditya van Vliet, Johannes |
| contents | A set $Ω\subset \mathbb{R}^d$ is said to be spectral if $L^2(Ω)$ admits an orthogonal basis of exponentials. While the product of spectral sets is known to be spectral, the converse fails in general. In this paper, we prove that the converse holds when one factor is a perturbation of an interval: if $E \subset [0,3/2 - ε]$ and $F$ are bounded sets of measure $1$, then $E \times F$ is spectral if and only if both $E$ and $F$ are spectral. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15159 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectrality of Product Sets with a Perturbed Interval Factor Ramabadran, Aditya van Vliet, Johannes Classical Analysis and ODEs 42C99 A set $Ω\subset \mathbb{R}^d$ is said to be spectral if $L^2(Ω)$ admits an orthogonal basis of exponentials. While the product of spectral sets is known to be spectral, the converse fails in general. In this paper, we prove that the converse holds when one factor is a perturbation of an interval: if $E \subset [0,3/2 - ε]$ and $F$ are bounded sets of measure $1$, then $E \times F$ is spectral if and only if both $E$ and $F$ are spectral. |
| title | Spectrality of Product Sets with a Perturbed Interval Factor |
| topic | Classical Analysis and ODEs 42C99 |
| url | https://arxiv.org/abs/2508.15159 |