Jackson核：分析球面上积分算子的eigenvalue序列衰变的工具
Jackson kernels: a tool for analyzing the decay of eigenvalue sequences of integral operators on the sphere
摘要：
正的和紧的积分算子的本征值序列的衰减率在文献中已经研究了很长时间。本文的重点是正积分算子作用于单位球面上的平方可积〔的〕，并由一个核生成，该核满足通过平均算子定义的Hölder型假设。在这里提出的方法中，衰减率将从算子本身的本征值的方便估计中获得，并借助于通过所谓的广义杰克逊核定义的通用近似算子的特定性质。衰变率的结构与赫尔德条件为经典条件时的衰变率结构相同。因此，在球面设置，这里介绍的抽象方法扩展了一些经典的结果的主题。
英文摘要：
Decay rates for the sequence of eigenvalues of positive and compact integral operators has been largely investigated for a long time in the literature. In this paper, the focus will be on positive integral operators acting on square integrable functions on the unit sphere and generated by a kernel satisfying a Hölder type assumption defined via average operators. In the approach to be presented here, the decay rates will be reached from convenient estimations on the eigenvalues of the operator themselves, with the help of specific properties of a generic approximation operator defined through the so-called generalized Jackson kernels. The decay rates have the same structure of those known to hold in the cases in which the Hölder condition is the classical one. Therefore, within the spherical setting, the abstract approach to be introduced here extends some classical results on the topic.
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