On the Stability of Sparse Convolutions
On the Stability of Sparse Convolutions
复制标题
DOI：
10.1016/j.acha.2015.08.002
复制
发表时间：
2014-09
期刊：
影响因子：
--
通讯作者：
Philipp Walk;P. Jung;G. Pfander
中科院分区：
文献类型：
--
作者：
Philipp Walk;P. Jung;G. Pfander
给出了Z等无挠离散Abel群G在ℓ2(G)×ℓ1(G)上的稀疏卷积的稳定性结果.结果表明，无挠性质阻止了稀疏序列卷积的完全抵消，从而允许建立稳定性，即具有泛范数界的内射性，它只依赖于序列的支撑基.这可以被看作是对稀疏卷积的Young不等式的相反表述。我们的结果取决于加性集合论中的一个压缩论点。
We give a stability result for sparse convolutions on ℓ 2 (G)× ℓ 1 (G) for torsion-free discrete Abelian groups G such as Z. It turns out, that the torsion-free property prevents full cancellation in the convolution of sparse sequences and hence allows to establish stability, that is, injectivity with an universal lower norm bound, which only depends on the support cardinalities of the sequences. This can be seen as a reverse statement of the Young inequality for sparse convolutions. Our result hinges on a compression argument in additive set theory.