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 construct new bases of real functions from $L^{2}\left(B_{r}\right)$ andfrom $L^{2}\left(\mathbb{Q}_{p}\right)$. These functions are eigenfunctions ofthe $p$-adic pseudo-differential Vladimirov operator, which is defined on acompact set $B_{r}\subset\mathbb{Q}_{p}$ of the field of $p$-adic numbers$\mathbb{Q}_{p}$ or, respectively, on the entire field $\mathbb{Q}_{p}$. Arelation between the basis of functions from $L^{2}\left(\mathbb{Q}_{p}\right)$and the basis of $p$-adic wavelets from $L^{2}\left(\mathbb{Q}_{p}\right)$ isfound. As an application, we consider the solution of the Cauchy problem withthe initial condition on a compact set for a pseudo-differential equation witha general pseudo-differential operator, which is diagonal in the basisconstructed.

On one real basis for $L^2(Q_p)$