论文标题
在Kantorovich-Rubinstein Norm中测得的Riesz基地和框架的签名
Sign intermixing for Riesz bases and frames measured in the Kantorovich-Rubinstein norm
论文作者
论文摘要
我们根据Kantorovich-Rubinstein Mose Mover Norm $ \ vert U_ {K} {k} \ vert_ {kr} $来测量$ l^{2} $空间中Bessel序列$（u_ {k}）$的标志交错现象。我们的主要观察结果表明，在定量上，减少$ \ vert u_ {k} \ vert_ {kr} \ longrightArrow 0 $ havily依赖S. Bernstein $ n $ - lipschitz功能的速度。特别是，这取决于测量空间的维度。我们在$ d $二维数据集对坎托洛维奇 - 罗宾斯坦框架的最差和最佳收敛速度方面取得了巨大的结果。这些费率很清晰。
We measure a sign interlacing phenomenon for Bessel sequences $ (u_{k})$ in $ L^{2}$ spaces in terms of the Kantorovich--Rubinstein mass moving norm $ \Vert u_{k}\Vert_{KR}$. Our main observation shows that, quantitatively, the rate of the decreasing $ \Vert u_{k}\Vert_{KR}\longrightarrow 0$ havily depends on S. Bernstein $ n$-widths of a compact of Lipschitz functions. In particular, it depends on the dimension of the measure space. We have sharp results on the worst and the best rate of convergence of Kantorovich--Rubinstein norms of frames on $d$-dimensional cube. Those rates are sharp.
