English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we present results on asymptotic characteristics ofmultivariate function classes in the uniform norm. Our main interest is theapproximation of functions with mixed smoothness parameter not larger than$1/2$. Our focus will be on the behavior of the best $m$-term trigonometricapproximation as well as the decay of Kolmogorov and entropy numbers in theuniform norm. It turns out that these quantities share a few fundamentalabstract properties like their behavior under real interpolation, such thatthey can be treated simultaneously. We start with proving estimates on finiterank convolution operators with range in a step hyperbolic cross. These resultsimply bounds for the corresponding function space embeddings by a well-knowndecomposition technique. The decay of Kolmogorov numbers have directimplications for the problem of sampling recovery in $L_2$ in situations whererecent results in the literature are not applicable since the correspondingapproximation numbers are not square summable.

Approximation of functions with small mixed smoothness in the uniform norm