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

We characterize the entire functions $P$ of $d$ variables, $d\ge 2,$ forwhich the $\mzd$-translates of $P\chi_{[0,N]^d}$ satisfy the partition of unityfor some $N\in \mn.$ In contrast to the one-dimensional case, these entirefunctions are not necessarily periodic. In the case where $P$ is atrigonometric polynomial, we characterize the maximal smoothness of$P\chi_{[0,N]^d},$ as well as the function that achieves it. A number ofespecially attractive constructions are achieved, e.g., of trigonometricpolynomials leading to any desired (finite) regularity for a fixed supportsize. As an application we obtain easy constructions of matrix-generated Gaborframes in $\ltrd,$ with small support and high smoothness. By sampling thisyields dual pairs of finite Gabor frames in $\ell^2(\mzd).$

On partition of unities generated by entire functions and Gabor frames in $\ltrd$ and $\ell^2(\mzd)$