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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We proved direct and inverse theorems on B-spline quasi-interpolation sampling representation with a Littlewood-Paley-type norm equivalence in Sobolev spaces \({W^{r}_{p}}\) of mixed smoothness r. Based on this representation, we established estimates of the approximation error of recovery in L  q -norm of functions from the unit ball \({U^{r}_{p}}\) in the spaces \({W^{r}_{p}}\) by linear sampling algorithms and the asymptotic optimality of these sampling algorithms in terms of Smolyak sampling width \({r^{s}_{n}}({U^{r}_{p}}, L_{q})\) and sampling width \(r_{n}({U^{r}_{p}}, L_{q})\).

B-Spline Quasi-Interpolation Sampling Representation and Sampling Recovery in Sobolev Spaces of Mixed Smoothness