论文标题
在周期性函数的卷积类别上按傅立叶总和均匀近似
Uniform approximations by Fourier sums on classes of convolutions of periodic functions
论文作者
论文摘要
我们在$2π$ - 周期函数上通过傅立叶总和来建立均匀近似值的精确上限的渐近估计，这些函数由空间的单位球的函数$φ（φ\ bot 1）$表示，$ l_ {1} $带有固定核的形式的$ l_ {1} $ $ψ_β（t）= \ sum \ limits_ {k = 1}^{\ infty}ψ（k）\ cos \ left（kt- \ frac {βπ} {2} {2} \ right）$，$ \ sum \ sum \ sum \ limits_ {k = 1} 0 $，$β\ in \ mathbb {r} $。
We establish asymptotic estimates for exact upper bounds of uniform approximations by Fourier sums on the classes of $2π$-periodic functions, which are represented by convolutions of functions $φ(φ\bot 1)$ from unit ball of the space $L_{1}$ with fixed kernels $Ψ_β$ of the form $Ψ_β(t)=\sum\limits_{k=1}^{\infty}ψ(k) \cos\left(kt-\frac{βπ}{2}\right)$, $\sum\limits_{k=1}^{\infty}kψ(k)<\infty$, $ψ(k)\geq 0$, $β\in\mathbb{R}$.
