论文标题
非架构径向演算：Volterra操作员和Laplace Transform
Non-Archimedean Radial Calculus: Volterra Operator and Laplace Transform
论文作者
论文摘要
在较早的论文（A. N. Kochubei，{\ itpacif。J.Math。} 269（2014），355--369）中，作者认为对Vladimirov的分数差异算子$ D^α$，$ d^α$，$α> 0 $的限制限制在非Archimedean Field上。特别是，发现它具有这样的右$ i^α$，以至于变量的适当更改将$ d^α$（用于径向函数）（用于径向函数）的方程式减少到具有类似经典Volterra方程的积分方程。换句话说，我们在非架构伪差异操作员的框架内发现，普通微分方程的对应物。在本文中，我们开始对操作员$ i^α$的操作者理论研究，并研究了拉普拉斯变换的相关类似物。
In an earlier paper (A. N. Kochubei, {\it Pacif. J. Math.} 269 (2014), 355--369), the author considered a restriction of Vladimirov's fractional differentiation operator $D^α$, $α>0$, to radial functions on a non-Archimedean field. In particular, it was found to possess such a right inverse $I^α$ that the appropriate change of variables reduces equations with $D^α$ (for radial functions) to integral equations whose properties resemble those of classical Volterra equations. In other words, we found, in the framework of non-Archimedean pseudo-differential operators, a counterpart of ordinary differential equations. In the present paper, we begin an operator-theoretic investigation of the operator $I^α$, and study a related analog of the Laplace transform.
