Schrödinger operators on the half-line with integrable complex potentials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909984963428352 |
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| author | Pushnitski, Alexander Štampach, František |
| author_facet | Pushnitski, Alexander Štampach, František |
| contents | In our previous work, we introduced the concept of a \emph{spectral pair} for a half-line Schrödinger operator with a \emph{complex} bounded potential $q$, serving as a substitute for the spectral measure in a non-self-adjoint setting. In this paper, we study the case of $q \in L^1(\mathbb{R}_+)$. We derive explicit formulas for the spectral pair in terms of the Jost solutions of a system of two equations naturally associated with the non-self-adjoint Schrödinger operator. A key component of our work, which is of independent interest, is the existence proof and analysis of these Jost solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05112 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Schrödinger operators on the half-line with integrable complex potentials Pushnitski, Alexander Štampach, František Spectral Theory 34L40, 37K15 In our previous work, we introduced the concept of a \emph{spectral pair} for a half-line Schrödinger operator with a \emph{complex} bounded potential $q$, serving as a substitute for the spectral measure in a non-self-adjoint setting. In this paper, we study the case of $q \in L^1(\mathbb{R}_+)$. We derive explicit formulas for the spectral pair in terms of the Jost solutions of a system of two equations naturally associated with the non-self-adjoint Schrödinger operator. A key component of our work, which is of independent interest, is the existence proof and analysis of these Jost solutions. |
| title | Schrödinger operators on the half-line with integrable complex potentials |
| topic | Spectral Theory 34L40, 37K15 |
| url | https://arxiv.org/abs/2601.05112 |