广义矩序列及其在若干矩偏微分方程中的应用
Sequences of generalized moments and their applications to some moment partial differential equations
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- Cardinal Stefan Wyszyński University（卡尔迪纳尔·斯特凡·维辛斯基大学）
- Shibaura Institute of Technology（芝浦工业大学）
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中文总结 AI 辅助
本文引入广义矩序列，推广Balser矩可和性理论，构造Laplace和Borel算子扩展，刻画矩偏微分方程可和解及其奇异方向跳跃，以超函数和核函数表达。
中文摘要 AI 辅助
我们引入了广义矩序列，它是保持可和性的序列以及来自Balser矩可和性理论的矩序列的推广。我们为这些新序列构造了Laplace和Borel积分算子的扩展。我们找到了广义矩的矩导数的积分表示。我们展示了具有广义矩的矩偏微分方程的可和解的刻画。我们描述了具有广义矩的矩偏微分方程的可和解的奇异方向，并表达了跨越这些奇异方向的跳跃，用超函数以及与保持可和性的序列相关联的核函数来表示，这些序列与给定的广义矩序列相连。
英文摘要
We introduce sequences of generalized moments that are a generalization of sequences preserving summability and sequences of moments from Balser's theory of moment summability. We construct extensions of Laplace and Borel integral operators for these new sequences. We find integral representations of moment derivatives for generalized moments. We show the characterization of summable solutions of moment-PDEs with generalized moments. We describe singular directions for summable solutions of moment-PDEs with generalized moments and we express jumps across these singular directions in terms of hyperfunctions and in terms of kernel functions associated with sequences preserving summability, which are connected with given sequences of generalized moments.
