组合图上Paley-Wiener空间的抽样
Sampling in paley-wiener spaces on combinatorial graphs
摘要：
在组合图上引入Paley-Wiener空间的概念。它表明，从这些空间中的一些功能是唯一确定的一些集的顶点，这是所谓的唯一性集上的值。这样的唯一性集描述的Poincare-Wirtinger型不等式。利用希尔伯特空间中框架的思想，提出了一种由唯一性集重构Paley-Wiener函数的算法。特别考虑到n维格，齐次树，本征值和本征函数问题的有限图。
英文摘要：
A notion of Paley-Wiener spaces is introduced on combinatorial graphs. It is shown that functions from some of these spaces are uniquely determined by their values on some sets of vertices which are called the uniqueness sets. Such uniqueness sets are described in terms of Poincare-Wirtingertype inequalities. A reconstruction algorithm of Paley-Wiener functions from uniqueness sets which uses the idea of frames in Hilbert spaces is developed. Special consideration is given to n-dimensional lattice, homogeneous trees, and eigenvalue and eigenfunction problems on finite graphs.
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