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

The goal of this paper is twofold. We prove that the operator $H=L+V$ , aperturbation of the Taibleson-Vladimirov multiplier $L=\mathfrak{D}^{\alpha}$by a potential $V(x)=b\left\Vert x\right\Vert ^{-\alpha},$ $b\geq b_{\ast},$ isessentially self-adjoint and non-negative definite (the critical value$b_{\ast}$ depends on $\alpha$ and will be specified later). While the operator$H$ is non-negative definite the potential $V(x)$ may well take negativevalues, e.g. $b_{\ast}<0$ for all $0<\alpha<1$. The equation $Hu=v$ admiits aGreen function $g_{H}(x,y)$, the integral kernel of the operator $H^{-1}$. Weobtain sharp lower- and upper bounds on the ratio of the functions $g_{H}(x,y)$and $g_{L}(x,y)$. Examples illustrate our exposition.

Hierarchical Schr\"{o}dinger-type operators: the case of potentials with local singularities