@Article{Rzepnicki2025,
author = "Rzepnicki, Łukasz",
title = "Integral representation of solutions to Dirac systems",
journal = "Opuscula Math.",
year = "2025",
volume = "45",
number = "3",
pages = "403--416",
doi = "https://doi.org/10.7494/OpMath.2025.45.3.403",
url = "https://doi.org/10.7494/OpMath.2025.45.3.403",
abstract = "We introduce a novel integral form for a fundamental set of solutions to one-dimensional Dirac systems with an integrable potential and spectral parameter \(\mu \in \mathbb{C}\). This method enables the construction of solutions that are analytic in \(\mu\) within the half-plane \(\operatorname{Im} \mu\gt -r\), \(r\geq 0\) and \(|\mu| \to \infty\). Consequently, we derive estimates for the solutions that remain valid not just within a horizontal strip but throughout the entire half-plane.",
keywords = "Dirac system, integrable potential, integral equations, fundamental system of solutions",
issn = "1232-9274"
}