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Browsing by Subject "fundamental system of solutions"

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    Item type:Article, Access status: Open Access ,
    Integral representation of solutions to Dirac systems
    (Wydawnictwa AGH, 2025) Rzepnicki, Łukasz
    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.