Harmonic functions for recurrent symmetric $α$-stable processeses with non-local perturbations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912590659059712 |
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| author | Tsuchida, Kaneharu |
| author_facet | Tsuchida, Kaneharu |
| contents | Let ${\mathbf M}$ be the recurrent symmetric (relativistic) $α$-stable process on ${\mathbb R}^d$. Let ${\mathcal H}^{μ+ F} (:= {\mathcal H} + μ+ F)$ be a Schrödinger type operator with local and non-local perturbations $μ$ and $F$. If $μ$ and $F$ satisfy suitable conditions associated with Kato class, we prove the existence of ground state for a Schrödinger type operator relating to ${\mathcal H}^{μ+ F}$. Furthermore, we prove the ground state becomes a probabilistically harmonic function of the Schrödinger operator generated by ${\mathcal H}^{μ+ F}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13918 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Harmonic functions for recurrent symmetric $α$-stable processeses with non-local perturbations Tsuchida, Kaneharu Probability 60J45 (Primary) 60J76, 31C25(Secondary) Let ${\mathbf M}$ be the recurrent symmetric (relativistic) $α$-stable process on ${\mathbb R}^d$. Let ${\mathcal H}^{μ+ F} (:= {\mathcal H} + μ+ F)$ be a Schrödinger type operator with local and non-local perturbations $μ$ and $F$. If $μ$ and $F$ satisfy suitable conditions associated with Kato class, we prove the existence of ground state for a Schrödinger type operator relating to ${\mathcal H}^{μ+ F}$. Furthermore, we prove the ground state becomes a probabilistically harmonic function of the Schrödinger operator generated by ${\mathcal H}^{μ+ F}$. |
| title | Harmonic functions for recurrent symmetric $α$-stable processeses with non-local perturbations |
| topic | Probability 60J45 (Primary) 60J76, 31C25(Secondary) |
| url | https://arxiv.org/abs/2509.13918 |