"s-Numbers of Embeddings of Weighted Wiener Classes"Sickel, WinfriedIn my talk I will discuss the behaviour of some $s$-numbers (including approximation numbers) of three different types of embeddings of the weighted Wiener algebra $A_w (\T)$ defined on the $d$-dimensional torus: \begin{itemize} \item $A_w (\T) \to A(\T)$, where $A(\T)$ denotes the Wiener algebra itself; \item $A_w (\T) \to L_2(\T)$; \item $A_w (\T) \to H^1(\T)$, where $w$ is given by \[ w (k) = w_{s,r} (k) := \left\{ \begin{array}{lll} \prod_{i=1}^d (1+|k_i|^r)^{s/r} &\qquad & \mbox{if}\quad 0 < r < \infty\, ; \\ &&\\ \prod_{i=1}^d \max (1,|k_i|)^{s} &\qquad & \mbox{if}\quad r = \infty\, . \end{array}\right. \] \end{itemize} It will be the main aim of my talk to describe the behaviour of the associated $s$-numbers in dependence of $n$ and the dimension $d$. This is joined work with Van Dung Ngyuen (Hanoi) and Van Kien Nguyen (Hanoi). |
| http://univie.ac.at/projektservice-mathematik/e/talks/Sickel_2022-04_abstract_strobl22.tex |
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