Wigner measures in the discrete setting: high-frequency analysis of sampling reconstruction operators
Fabricio Macia
本文的目标是了解R^d中一系列函数产生的振荡和浓度效应如何通过采样和重建操作符对常规网格的作用进行修改。 我们的分析是在Wigner和缺陷测量方面进行的,该测量提供了L^2(mathbbR^d)中边界序列的高频行为的定量描述。 我们实际上提出了明确的公式,使计算采样/重建序列的此类测量成为可能。 因此,我们能够表征保存或过滤特定序列类的高频行为的采样和重建运算符。 我们结果的证明依赖于与离散函数序列相关的Wigner度量的构造和操作。
The goal of this article is that of understanding how the oscillation and concentration effects developed by a sequence of functions in ℝ^d are modified by the action of Sampling and Reconstruction operators on regular grids. Our analysis is performed in terms of Wigner and defect measures, which provide a quantitative description of the high frequency behavior of bounded sequences in L^2(mathbbR^d). We actually present explicit formulas that make possible to compute such measures for sampled/re...