论文标题
$ s $ - 加权维也纳代数的嵌入
$s$-Numbers of Embeddings of Weighted Wiener Algebras
论文作者
论文摘要
在本文中，我们研究了Kolmogorov，近似，Bernstein和Weyl的渐近行为，嵌入$ \ Mathcal {a}^{s，r} _ {\ rm mix}（\ Mathbbbb {t}^d） $ \ MATHCAL {a}^{s，r} _ {\ rm mix}（\ Mathbb {t}^d） Mix}（\ MathBb {T}^D）$是混合平滑度$ S $和$ \ Mathcal {a}（\ Mathbb {t}^d）$的加权Wiener代数，是Wiener代数本身，都定义在$ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ - d $ d $ d $ d $ dorus $ \ mathbbbbbbbbbbbbbbbbbbbb {我们的主要利益在于计算相关的渐近常数。
In this paper we study the asymptotic behavior of Kolmogorov, approximation, Bernstein and Weyl numbers of embeddings $ \mathcal{A}^{s,r}_{\rm mix}(\mathbb{T}^d) \to L_2(\mathbb{T}^d)$ and $\mathcal{A}^{s,r}_{\rm mix}(\mathbb{T}^d) \to \mathcal{A}(\mathbb{T}^d)$, where $\mathcal{A}^{s,r}_{\rm mix}(\mathbb{T}^d)$ is a weighted Wiener algebra of mixed smoothness $s$ and $\mathcal{A}(\mathbb{T}^d)$ is the Wiener algebra itself, both defined on the $d$-dimensional torus $\mathbb{T}^d$. Our main interest consists in the calculation of the associated asymptotic constants.
