Compactness properties of weighted summation operators on trees - the critical case
Compactness properties of weighted summation operators on trees - the critical case
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树上加权求和算子的紧致性性质 - 关键情况
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
W. Linde
中科院分区：
文献类型：
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作者：
M. Lifshits;W. Linde
本文的目的是给出临界情况下树上求和算子的熵数的上界。在最近的一篇论文[10]中，我们详细阐述了一般树上加权求和算子的框架，其中我们将算子的熵与配备了适当度量的基础树的熵联系起来。然而，在熵行为的关键情况下，结果是不完整的，因为这种情况需要更复杂的技术。在本文中，我们将填补[10]中留下的空白。为此，我们发展了一种方法，工作在一般树和一般加权求和算子的上下文中，这是最近在[9]中提出的，用于二叉树上的特定临界算子。在研究某些Volterra积分算子在临界情况下的紧性时，这些问题自然地出现了。
The aim of this paper is to provide upper bounds for the entropy numbers of summation operators on trees in a critical case. In a recent paper [10] we elaborated a framework of weighted summation operators on general trees where we related the entropy of the operator with those of the underlying tree equipped with an appropriate metric. However, the results were left incomplete in a critical case of the entropy behavior, because this case requires much more involved techniques. In the present article we fill the gap left open in [10]. To this end we develop a method, working in the context of general trees and general weighted summation operators, which was recently proposed in [9] for a particular critical operator on the binary tree. Those problems appeared in natural way during the study of compactness properties of certain Volterra integral operators in a critical case.