Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.23754 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918369380270080 |
|---|---|
| author | Chakraborty, Piyali Dutkay, Dorin Ervin |
| author_facet | Chakraborty, Piyali Dutkay, Dorin Ervin |
| contents | In relation to Fuglede's conjecture, we establish several Plancherel-type identities and demonstrate the surjectivity of the Fourier transform between certain unbounded tiling sets of $\mathbb{R}$ that are in duality. In the terminology commonly used in the context of Fuglede's conjecture, our result states that an open set tiles $\mathbb{R}$ by the finite set $\{0,1,\dots,p-1\}$ if and only if it admits a spectrum (or, equivalently, a dual pair measure) given by the Lebesgue measure on $\left[-\tfrac{1}{2p}, \tfrac{1}{2p}\right] + \mathbb{Z}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23754 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some Plancherel identities for unbounded subsets of $\mathbb R$ in duality Chakraborty, Piyali Dutkay, Dorin Ervin Functional Analysis 47E05, 42A16 In relation to Fuglede's conjecture, we establish several Plancherel-type identities and demonstrate the surjectivity of the Fourier transform between certain unbounded tiling sets of $\mathbb{R}$ that are in duality. In the terminology commonly used in the context of Fuglede's conjecture, our result states that an open set tiles $\mathbb{R}$ by the finite set $\{0,1,\dots,p-1\}$ if and only if it admits a spectrum (or, equivalently, a dual pair measure) given by the Lebesgue measure on $\left[-\tfrac{1}{2p}, \tfrac{1}{2p}\right] + \mathbb{Z}$. |
| title | Some Plancherel identities for unbounded subsets of $\mathbb R$ in duality |
| topic | Functional Analysis 47E05, 42A16 |
| url | https://arxiv.org/abs/2510.23754 |