关于Borel求和相对于ODEs和薄纱积分的正则性
The Regularity of ODEs and Thimble Integrals with Respect to Borel Summation
AI总结：
本文通过Borel求和探讨ODEs和薄纱积分的正则性，揭示其与Borel平面特殊点的关系，并举例说明相关问题的解的正则性。
摘要：
通过Borel求和，人们通常可以从问题的渐近展开式中重建出解析解。我们将Borel求和的有效性视为解的正则性属性，并证明某些微分方程和积分问题的解在这一意义上是正则的。通过从几何视角看待拉普拉斯和Borel变换，我们还阐明了为什么“Borel正则”解与Borel平面上的特殊点相关联。我们特别考虑的是一类水平1的ODEs和一维Lefschetz薄纱上的指数周期积分。为了扩大文献中可用示例的种类，我们对这些问题的各种实例进行了详细讨论。
英文摘要：
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 equation 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
