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

In this article we study the notion of capacity of a vertex for infinitegraphs over non-Archimedean fields. In contrast to graphs over the real fieldmonotone limits do not need to exist. Thus, in our situation next to positiveand null capacity there is a third case of divergent capacity. However, we showthat either of these cases is independent of the choice of the vertex and istherefore a global property for connected graphs. The capacity is shown toconnect the minimization of the energy, solutions of the Dirichlet problem andexistence of a Green's function. We furthermore give sufficient criteria inform of a Nash-Williams test, study the relation to Hardy inequalities anddiscuss the existence of positive superharmonic functions. Finally, weinvestigate the analytic features of the transition operator in relation to theinverse of the Laplace operator.

Capacity of infinite graphs over non-Archimedean ordered fields