Sonine 条件的一个等价表述
An equivalent formulation of Sonine condition
AI总结：
本文提出更一般的 Sonine 条件（gSC），并证明其与原始条件等价，表明 Sonine 核可由与关联核在起始点的卷积行为刻画。
摘要：
Sonine 核由 Sonine 条件（记为 SC）刻画，是非局部微分方程和积分方程中一类重要的核。本文提出了一个更具一般形式的 SC（记为 gSC），它比 SC 更方便地适应复杂的核与方程。给出了一个典型核，并据此将 gSC 下第一类 Volterra 积分方程进行变换并分析。基于这些结果，最终证明了 gSC 确实与原始 SC 等价，这表明 Sonine 核本质上可由其与关联核在起始点的卷积行为来刻画。
英文摘要：
Sonine kernel is characterized by the Sonine condition (denoted by SC) and is an important class of kernels in nonlocal differential equations and integral equations. This work proposes a SC with a more general form (denoted by gSC), which is more convenient than SC to accommodate complex kernels and equations. A typical kernel is given, and the first-kind Volterra integral equation under gSC is accordingly transformed and then analyzed. Based on these results, it is finally proved that the gSC is indeed equivalent to the original SC, which indicates that the Sonine kernel may be essentially characterized by the behavior of its convolution with the associated kernel at the starting point.
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