发表机构
King Fahd University of Petroleum and Minerals（法赫德国王石油与矿产大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对Lévy型伪微分算子驱动的Cauchy问题，将解的存在唯一性推广至更广初始条件，并利用广义费曼图展开解及其对数，建立Borel可和性，以一维Lévy-高斯例示。
AI 中文摘要
我们研究了一类由具有Lévy型符号的伪微分算子驱动的Cauchy问题。我们将先前从指数初始数据得到的结果推广到更广泛的初始条件集合。我们证明了解的存在性和唯一性，该解具有与相关核的显式卷积表示。然后，我们推导了解的一个渐近展开，其系数用矩表示，并在取对数后用累积量表示。这些展开通过广义费曼图表示来组织，为解及其对数提供了清晰的组合描述。我们还建立了在适当条件下的Borel可和性结果，并将经典的指数情形作为特例恢复。最后，我们通过一个一维Lévy-高斯例子来说明卷积核和解。
英文摘要
We study a class of Cauchy problems driven by pseudo-differential operators with Lévy-type symbols. We extend earlier results from exponential initial data to a broader set of initial conditions. We demonstrate the existence and uniqueness of the solution, which has an explicit convolution representation with the associated kernel. We then derive an asymptotic expansion of the solution, with coefficients expressed in terms of moments and, after taking logarithms, in terms of cumulants. These expansions are organized through generalized Feynman graph representations, providing a clear combinatorial description of both the solution and its logarithm. We also establish a Borel summability result under suitable conditions and recover the classical exponential case as a special instance. Finally, we illustrate the convolution kernel and solution through a one-dimensional Lévy-Gaussian example.
