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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2604.12997 |
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| _version_ | 1866911593188556800 |
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| author | Motta, Ricardo |
| author_facet | Motta, Ricardo |
| contents | We establish sufficient conditions on discrete subsets of $\mathbb{R}^d$ for them to form a uniqueness or a non-uniqueness pair for the fractional Laplacian. Specifically, assuming that $f=0$ on $Λ$ and that $(-Δ)^sf=0$ on $M$, where $Λ, M \subset \mathbb{R}^d$ are discrete, we find sufficient conditions on these sets that force $f$ to vanish identically, and we provide examples in which non-uniqueness occurs. Some of the ideas used in the proofs also extend to a broader class of multiplier operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_12997 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Uniqueness and non-uniqueness pairs for the fractional Laplacian Motta, Ricardo Classical Analysis and ODEs Analysis of PDEs 42B10 We establish sufficient conditions on discrete subsets of $\mathbb{R}^d$ for them to form a uniqueness or a non-uniqueness pair for the fractional Laplacian. Specifically, assuming that $f=0$ on $Λ$ and that $(-Δ)^sf=0$ on $M$, where $Λ, M \subset \mathbb{R}^d$ are discrete, we find sufficient conditions on these sets that force $f$ to vanish identically, and we provide examples in which non-uniqueness occurs. Some of the ideas used in the proofs also extend to a broader class of multiplier operators. |
| title | Uniqueness and non-uniqueness pairs for the fractional Laplacian |
| topic | Classical Analysis and ODEs Analysis of PDEs 42B10 |
| url | https://arxiv.org/abs/2604.12997 |