Direct and inverse approximation theorems of $2π$-periodic functions by Taylor--Abel--Poisson means

Approximation theorems for multivariate Taylor-Abel-Poisson means

We obtain direct and inverse approximation theorems of functions of several variables by Taylor-Abel-Poisson means in the integral metrics. We also show that norms of multipliers in the spaces $L_{p,Y}(\mathbb T^d)$ are equivalent for all positive integers $d.$

在六边形区域上通过Taylor-Abel-Poisson平均进行逼近

Approximation on hexagonal domains by Taylor-Abel-Poisson means

本文研究了积分度量下关于六边形区域周期的多元函数Fourier级数的Taylor-Abel-Poisson线性求和法的逼近性质，证明了直接和逆定理，并得到了Poisson核高阶径向导数$L_1$-范数的Bernstein型不等式。

Uncertainty product of the spherical Abel-Poisson wavelet

In the present paper, the variances in the space and momentum domains of the spherical Abel-Poisson wavelet, as well as the limit of the uncertainty product for $ρ\to0$, where $ρ$ is the scale parameter, are computed. The values of these quantities coincide with a certain accuracy with those of the spherical Poisson wavelet with $\tfrac{1}{2}$ substituted for the order parameter.

关于六角形傅里叶级数的Cesàro与Abel-Poisson平均

On Cesàro and Abel-Poisson Means of Hexagonal Fourier Series

该文研究六角形傅里叶级数的Cesàro与Abel-Poisson平均的逼近性质，借助连续模估计六角格上连续周期函数的对应级数平均的逼近阶。

Exact estimation of an approximation of some classes of differentiable functions by convolution operators

Nikol'skii known theorem for the kernels satisfying a condition $A^*_n$, is proved and for kernels from wider class. Explicit formulas for calculating the value of an approximation of classes $\W^{r, β}_{p, n} $ by convolution operators of special form are obtained. Here $ β\in\Z $, $r> 0 $, $n\in\N $, and $p=1 $ or $p =\infty $. As particular cases obtained explicit formulas for value of an approximation of the indicated classes generalized Abel-Poisson means, biharmonic operators of Poisson, Cesaro and Riesz means. In some cases for value of an approximation of the indicated classes asymptot…