On the Unique Continuation Principle for a Class of Translation Invariant Nonlocal Operators
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866915911654440960 |
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| author | Berger, David Schilling, Rene L. |
| author_facet | Berger, David Schilling, Rene L. |
| contents | The unique continuation property (UCP) for an operator $A$ says that, if $Au = 0 = u$ holds on an open set $G$, then one has $u=0$ everywhere. We establish necessary and sufficient conditions for the UCP for the class of Lévy operators. We prove a connection between the UCP of the Lévy operator and its resolvent. Our results are applied to obtain a new elementary proof of the UCP for the fractional Laplace operator, and for certain functions (Bernstein functions) of the discrete Laplace operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_02357 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Unique Continuation Principle for a Class of Translation Invariant Nonlocal Operators Berger, David Schilling, Rene L. Functional Analysis Analysis of PDEs Probability The unique continuation property (UCP) for an operator $A$ says that, if $Au = 0 = u$ holds on an open set $G$, then one has $u=0$ everywhere. We establish necessary and sufficient conditions for the UCP for the class of Lévy operators. We prove a connection between the UCP of the Lévy operator and its resolvent. Our results are applied to obtain a new elementary proof of the UCP for the fractional Laplace operator, and for certain functions (Bernstein functions) of the discrete Laplace operator. |
| title | On the Unique Continuation Principle for a Class of Translation Invariant Nonlocal Operators |
| topic | Functional Analysis Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2604.02357 |