Schrödinger operators on the half-line with integrable complex potentials

Alexander Pushnitski; František Štampach

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arXiv · 2601.05112

Schrödinger operators on the half-line with integrable complex potentials

Alexander Pushnitski·František Štampach

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Abstract

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.

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BibTeX RIS

Alexander Pushnitski, František Štampach. 2026-01-08. Schrödinger operators on the half-line with integrable complex potentials. https://arxiv.org/abs/2601.05112

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