论文标题
单个函数翻译的线性组合近似
Approximation by linear combinations of translates of a single function
论文作者
论文摘要
我们通过$ n $的任意线性组合来研究近似，这是定期函数的单个函数。我们构建了该近似值的一些线性方法，用于由单个函数引起的卷积引起的单变量函数，并通过这些方法证明$ l^p $ - approximation收敛速率，当$ n \ to \ infty $，以$ 1 \ leq p \ leq p \ leq p \ leq \ lef infty $。我们还将这些结果推广到多元函数类别的类别，以单个函数的张量产物定义了卷积。在此类$ p = 2 $的情况下，我们还证明了$ n $的任意线性组合的最佳近似值的数量的下限，是任意功能的转换。
We study approximation by arbitrary linear combinations of $n$ translates of a single function of periodic functions. We construct some linear methods of this approximation for univariate functions in the class induced by the convolution with a single function, and prove upper bounds of the $L^p$-approximation convergence rate by these methods, when $n \to \infty$, for $1 \leq p \leq \infty$. We also generalize these results to classes of multivariate functions defined the convolution with the tensor product of a single function. In the case $p=2$, for this class, we also prove a lower bound of the quantity characterizing best approximation of by arbitrary linear combinations of $n$ translates of arbitrary function.
