Resolvent estimates for one-dimensional Schrödinger operators with complex potentials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866908492333318144 |
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| author | Arnal, Antonio Siegl, Petr |
| author_facet | Arnal, Antonio Siegl, Petr |
| contents | We study one-dimensional Schrödinger operators $\operatorname{H} = -\partial_x^2 + V$ with unbounded complex potentials $V$ and derive asymptotic estimates for the norm of the resolvent, $Ψ(λ) := \| (\operatorname{H} - λ)^{-1} \|$, as $|λ| \to +\infty$, separately considering $λ\in \operatorname{Ran} V$ and $λ\in \mathbb{R}_+$. In each case, our analysis yields an exact leading order term and an explicit remainder for $Ψ(λ)$ and we show these estimates to be optimal. We also discuss several extensions of the main results, their interrelation with some aspects of semigroup theory and illustrate them with examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_15938 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Resolvent estimates for one-dimensional Schrödinger operators with complex potentials Arnal, Antonio Siegl, Petr Spectral Theory Mathematical Physics Functional Analysis 34L40, 35P20, 47A10, 81Q12 We study one-dimensional Schrödinger operators $\operatorname{H} = -\partial_x^2 + V$ with unbounded complex potentials $V$ and derive asymptotic estimates for the norm of the resolvent, $Ψ(λ) := \| (\operatorname{H} - λ)^{-1} \|$, as $|λ| \to +\infty$, separately considering $λ\in \operatorname{Ran} V$ and $λ\in \mathbb{R}_+$. In each case, our analysis yields an exact leading order term and an explicit remainder for $Ψ(λ)$ and we show these estimates to be optimal. We also discuss several extensions of the main results, their interrelation with some aspects of semigroup theory and illustrate them with examples. |
| title | Resolvent estimates for one-dimensional Schrödinger operators with complex potentials |
| topic | Spectral Theory Mathematical Physics Functional Analysis 34L40, 35P20, 47A10, 81Q12 |
| url | https://arxiv.org/abs/2203.15938 |