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 Tools annual

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 monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We find the necessary and sufficient conditions for refinable step functionunder which this function generates an orthogonal MRA in the $L_2(\mathfrak G)$-spaces on Vilenkin groups $\mathfrak G$. We consider a class of refinable stepfunctions for which the mask $m_0(\chi)$ is constant on cosets $\mathfrakG_{-1}^\bot$ and its modulus $|m_0(\chi)|$ takes two values only: 0 and 1. Wewill prove that any refinable step function $\varphi$ from this class thatgenerates an orthogonal MRA on $p$-adic Vilenkin group $\mathfrak G$ hasFourier transform with condition ${\rm supp} \hat \varphi(\chi)\subset\mathfrak G_{p-2}^\bot$. We show the sharpness of this result too.

Step refinable functions and orthogonal MRA on $p$-adic Vilenkin groups