The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation
Through Borel summation, one can often reconstruct an analytic solution of a problem from its asymptotic expansion. We view the effectiveness of Borel summation as a regularity property of the solution, and we show that the solutions of certain differential equations and integration problems are reg...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2025 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2025
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/214180 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation. Veronica Fantini and Aaron Fenyes. SIGMA 21 (2025), 101, 69 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Through Borel summation, one can often reconstruct an analytic solution of a problem from its asymptotic expansion. We view the effectiveness of Borel summation as a regularity property of the solution, and we show that the solutions of certain differential equations and integration problems are regular in this sense. By taking a geometric perspective on the Laplace and Borel transforms, we also clarify why ''Borel regular'' solutions are associated with special points on the Borel plane. The particular classes of problems we look at are level 1 ODEs and exponential period integrals over one-dimensional Lefschetz thimbles. To expand the variety of examples available in the literature, we treat various examples of these problems in detail.
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| ISSN: | 1815-0659 |