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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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2025-05-01
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| Series: | Opuscula Mathematica |
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| Online Access: | https://www.opuscula.agh.edu.pl/vol45/3/art/opuscula_math_4519.pdf |
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| _version_ | 1849761624952406016 |
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| author | Łukasz Rzepnicki |
| author_facet | Łukasz Rzepnicki |
| author_sort | Łukasz Rzepnicki |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a29795abfa8045879e83c2194c57dc21 |
| institution | DOAJ |
| issn | 1232-9274 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj-art-a29795abfa8045879e83c2194c57dc212025-08-20T03:05:57ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742025-05-01453403416https://doi.org/10.7494/OpMath.2025.45.3.4034519Integral representation of solutions to Dirac systemsŁukasz Rzepnicki0https://orcid.org/0000-0001-8532-6680Nicolaus Copernicus University in Toruń, Faculty of Mathematics and Computer Science, Chopina 12/18, 87-100 Toruń, PolandWe 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.https://www.opuscula.agh.edu.pl/vol45/3/art/opuscula_math_4519.pdfdirac systemintegrable potentialintegral equationsfundamental system of solutions |
| spellingShingle | Łukasz Rzepnicki Integral representation of solutions to Dirac systems Opuscula Mathematica dirac system integrable potential integral equations fundamental system of solutions |
| title | Integral representation of solutions to Dirac systems |
| title_full | Integral representation of solutions to Dirac systems |
| title_fullStr | Integral representation of solutions to Dirac systems |
| title_full_unstemmed | Integral representation of solutions to Dirac systems |
| title_short | Integral representation of solutions to Dirac systems |
| title_sort | integral representation of solutions to dirac systems |
| topic | dirac system integrable potential integral equations fundamental system of solutions |
| url | https://www.opuscula.agh.edu.pl/vol45/3/art/opuscula_math_4519.pdf |
| work_keys_str_mv | AT łukaszrzepnicki integralrepresentationofsolutionstodiracsystems |