Approximation by sampling-type operators in $L_p$-spaces

$L_p(\Bbb{R}^d)$ 中采样算子逼近的光滑性特殊度量

Special measures of smoothness for approximation by sampling operators in $L_p(\Bbb{R}^d)$

针对低光滑函数传统度量失效问题，提出结合采样点局部行为的改进光滑性度量，为 $L_p$ 空间采样算子逼近提供匹配的正逆误差估计及收敛准则。

Sharp $L_p$-error estimates for sampling operators

We study approximation properties of linear sampling operators in the spaces $L_p$ for $1\le p<\infty$. By means of the Steklov averages, we introduce a new measure of smoothness that simultaneously contains information on the smoothness of a function in $L_p$ and discrete information on the behaviour of a function at sampling points. The new measure of smoothness enables us to improve and extend several classical results of approximation theory to the case of linear sampling operators. In particular, we obtain matching direct and inverse approximation inequalities for sampling operators in $L…

Banach空间中线性采样算子的逼近

Approximation by linear sampling operators in Banach spaces

本文研究Banach空间中线性采样算子的逼近性质，推导了新的逼近估计和等价结果，扩展了经典定理的应用范围。

操作员的不规则多通道抽样

Irregular and multi--channel sampling of operators

带限函数的经典采样定理最近被推广到所谓的带限算子，即带限Kohn-Nirenberg符号的算子。在这里，我们讨论了经典采样定理的两个最核心的扩展算子采样版本。在不规则算子采样中，采样集不是具有均匀距离的周期。在多通道算子采样中，我们通过多个算子采样输出获得关于一个算子的完整信息。

Sampling of operators

Sampling and reconstruction of functions is a central tool in science. A key result is given by the sampling theorem for bandlimited functions attributed to Whittaker, Shannon, Nyquist, and Kotelnikov. We develop an analogous sampling theory for operators which we call bandlimited if their Kohn-Nirenberg symbols are bandlimited. We prove sampling theorems for such operators and show that they are extensions of the classical sampling theorem.

Approximation of Discontinuous Signals by Exponential Sampling Series

We analyse the behaviour of the exponential sampling series $S_{w}^χf$ at jump discontinuity of the bounded signal $f.$ We obtain a representation lemma that is used for analysing the series $S_{w}^χf$ and we establish approximation of jump discontinuity functions by the series $S_{w}^χf.$ The rate of approximation of the exponential sampling series $S_{w}^χf$ is obtained in terms of logarithmic modulus of continuity of functions and the round-off and time-jitter errors are also studied. Finally we give some graphical representation of approximation of discontinuous functions by $S_{w}^χf$ usi…