Superoscillating Sequences Towards Approximation in or -Type Spaces and Extrapolation
Superoscillating Sequences Towards Approximation in or -Type Spaces and Extrapolation
复制标题
超振荡序列在 or 型空间中的逼近和外推
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
A. Yger
中科院分区：
文献类型：
--
作者：
F. Colombo;D. Struppa;A. Yger
Aharonov-Berry超振荡是频带有限的函数序列，其振荡速度恰好比其最快的傅立叶分量更快。本文分析了Schwartz空间S(R，C)或其某些子空间中的函数、调和分布或超分布在紧集或相对紧开集(取决于上下文)上可以在何种意义下被这种超振荡序列逼近。我们还展示了如何从这种序列的存在中获益，以便从实际线路的给定段中外推具有有限能量的带限信号。
Aharonov–Berry superoscillations are band-limited sequences of functions that happen to oscillate asymptotically faster than their fastest Fourier component. In this paper we analyze in what sense functions in the Schwartz space S (R, C) or in some of its subspaces, tempered distributions or also ultra-distributions, could be approximated over compact sets or relatively compact open sets (depending on the context) by such superoscillating sequences. We also show how one can profit of the existence of such sequences in order to extrapolate band-limited signals with finite energy from a given segment of the real line.