加权上确界范数下傅里叶-拉盖尔级数的正则化求和
Regularized summation of Fourier-Laguerre series in the weighted sup-norm
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中文总结 AI 辅助
该研究针对半直线上函数恢复问题，提出基于拉盖尔多项式的正则化求和方法，分析其在维纳类函数上的逼近性质，证明该方法稳定且在加权上确界范数精度及傅里叶-拉盖尔系数数量上均达阶最优。
中文摘要 AI 辅助
我们考虑从非精确输入信息中恢复半直线上定义的函数的问题。针对所提出的基于拉盖尔多项式的正则化求和方法，我们分析其在维纳类函数上的逼近性质。我们确定了这些方法对输入数据的微小扰动具有稳定性的条件，且该方法不仅在加权$\text{sup}$-范数的精度上达到阶最优，还在所用傅里叶-拉盖尔系数的数量上达到阶最优。
英文摘要
We consider the problem of recovering functions defined on the half-line from inexact input information. For the proposed regularizing summation methods based on Laguerre polynomials, we analyze their approximation properties on functions from Wiener classes. We establish conditions under which these methods are stable with respect to small perturbations of the input data and order-optimal not only in accuracy in the weighted $\sup$-norm, but also in the number of Fourier-Laguerre coefficients used.
