Irrational series I Laplace transform in a neighborhood of $-\infty$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912951777099776 |
|---|---|
| author | Thom, Olivier |
| author_facet | Thom, Olivier |
| contents | Discrete sums of exponentials $g(w) = \sum a_β \mathrm{e}^{βw}$ with positive exponents may converge not normally in neighborhoods $H$ of $-\infty$ which do not contain half-planes. In order to obtain a decomposition of a holomorphic function $g$ in $H$ as a sum of exponentials we study the Laplace transform in general neighborhoods of $-\infty$.
We adress questions such as continuity of Laplace and inverse Laplace transformations, continuity for the operation of taking partial sums, and resummation formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07347 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Irrational series I Laplace transform in a neighborhood of $-\infty$ Thom, Olivier Complex Variables 30E20 (Primary) 44A10, 46F15 (Secondary) Discrete sums of exponentials $g(w) = \sum a_β \mathrm{e}^{βw}$ with positive exponents may converge not normally in neighborhoods $H$ of $-\infty$ which do not contain half-planes. In order to obtain a decomposition of a holomorphic function $g$ in $H$ as a sum of exponentials we study the Laplace transform in general neighborhoods of $-\infty$. We adress questions such as continuity of Laplace and inverse Laplace transformations, continuity for the operation of taking partial sums, and resummation formulas. |
| title | Irrational series I Laplace transform in a neighborhood of $-\infty$ |
| topic | Complex Variables 30E20 (Primary) 44A10, 46F15 (Secondary) |
| url | https://arxiv.org/abs/2603.07347 |