Integral representation of solutions to Dirac systems
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}...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
AGH Univeristy of Science and Technology Press
2025-05-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | https://www.opuscula.agh.edu.pl/vol45/3/art/opuscula_math_4519.pdf |
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| Summary: | 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. |
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| ISSN: | 1232-9274 |