TY  - JOUR
ID  - Rzepnicki2025
LB  - Rzepnicki2025
AU  - Rzepnicki, Łukasz
TI  - Integral representation of solutions to Dirac systems
ST  - Integral representation of solutions to Dirac systems
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2025
VL  - 45
IS  - 3
SP  - 403
EP  - 416
DO  - https://doi.org/10.7494/OpMath.2025.45.3.403
UR  - https://doi.org/10.7494/OpMath.2025.45.3.403
AB  - 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.
KW  - Dirac system
KW  - integrable potential
KW  - integral equations
KW  - fundamental system of solutions
SN  - 1232-9274
ER  -