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Browsing by Subject "Dirac system"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Direct and inverse spectral problems for Dirac systems with nonlocal potentials
    (Wydawnictwa AGH, 2019) Dębowska, Kamila; Nižnik, Leonid Pavlovič
    The main purposes of this paper are to study the direct and inverse spectral problems of the one-dimensional Dirac operators with nonlocal potentials. Based on informations about the spectrum of the operator, we find the potential and recover the form of the Dirac system. The methods used allow us to reduce the situation to the one-dimensional case. In accordance with the given assumptions and conditions we consider problems in a specific way. We describe the spectrum, the resolvent, the characteristic function etc. Illustrative examples are also given.
  • thumbnail.journal.alt
    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.