论文标题
部分可观测时空混沌系统的无模型预测
End-point Norm Estimates for Cesàro and Copson Operators
论文作者
论文摘要
对于在加权$ \ ell^\ infty $空间之间作用的大量运算符，为其规范和对非负序列锥的限制提供了精确的公式；非负序列；和非负责序列。所涉及的权重是任意的非负序列，在域和代码域空间上可能有所不同。结果适用于Cesàro和Copson运营商，将其规范和距离及其距离提供给整个空间和锥体上的身份操作员。这些公式的简化是在这些操作员以功率加权$ \ ell^\ infty $的情况下得出的。作为应用程序，最佳常数是针对Cesàro的加权$ \ ell^\ infty $ norms and Copson操作员的最佳常数。
For a large class of operators acting between weighted $\ell^\infty$ spaces, exact formulas are given for their norms and the norms of their restrictions to the cones of nonnegative sequences; nonnegative, nonincreasing sequences; and nonnegative, nondecreasing sequences. The weights involved are arbitrary nonnegative sequences and may differ in the domain and codomain spaces. The results are applied to the Cesàro and Copson operators, giving their norms and their distances to the identity operator on the whole space and on the cones. Simplifications of these formulas are derived in the case of these operators acting on power-weighted $\ell^\infty$. As an application, best constants are given for inequalities relating the weighted $\ell^\infty$ norms of the Cesàro and Copson operators both for general weights and for power weights.
