论文标题
关于雅各比级系数的亚伯方程解决方案的平滑度
On Smoothness of the Abel Equation Solution in Terms of the Jacoby Series Coefficients
论文作者
论文摘要
在本文中，我们继续研究ABEL方程，正确的部分属于Lebesgue加权空间。我们改善了先前已知的结果 - 根据雅各比级数系数的唯一性和存在定理，这使我们有机会找到和分类解决方案，这是由于某些关系包含右侧的雅各比系数的渐近性。新的主要结果如下：对参数施加的条件，在该参数下，ABEL方程在该参数下具有由系列代表的独特解决方案；建立了参数值与解决方案平滑度之间的关系。证明了参数之一和解决方案的平滑度之间的独立性。
In this paper we continue the investigation of the Abel equation with the right part belonging to a Lebesgue weighted space. We have improved the previously known result - the uniqueness and existence theorem formulated in terms of the Jacoby series coefficients that gives us an opportunity to find and classify a solution due to an asymptotic of some relation containing the Jacoby coefficients of the right part. The new main results are in the following: The conditions imposed on the parameters, under which the Abel equation has a unique solution represented by the series, are formulated; The relationship between the values of the parameters and the solution smoothness is established. The independence between one of the parameters and the smoothness of the solution is proved.
