Regular singular Volterra equations on complex domains
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917904371417088 |
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| author | Fantini, Veronica Fenyes, Aaron |
| author_facet | Fantini, Veronica Fenyes, Aaron |
| contents | The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular singularities can become a Volterra equation with regular singularities. It can also reveal hidden structure, especially when the Volterra equation extends to a complex domain. Our main result is to show that for a certain kind of regular singular Volterra equation on a complex domain, there is always a unique solution of a certain form. As a motivating example, this kind of Volterra equation arises when using Laplace transform methods to solve a level 1 differential equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00603 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regular singular Volterra equations on complex domains Fantini, Veronica Fenyes, Aaron Classical Analysis and ODEs The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular singularities can become a Volterra equation with regular singularities. It can also reveal hidden structure, especially when the Volterra equation extends to a complex domain. Our main result is to show that for a certain kind of regular singular Volterra equation on a complex domain, there is always a unique solution of a certain form. As a motivating example, this kind of Volterra equation arises when using Laplace transform methods to solve a level 1 differential equation. |
| title | Regular singular Volterra equations on complex domains |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2309.00603 |