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 consider two operators $A_{0},B_{0}$ between two Hilbert spaces satisfying$A_{0}\subseteq-B_{0}^{\ast}$ and $B_{0}\subseteq-A_{0}^{\ast}$ and inspectextensions $A^{\#}$ and $B^{\#}$ of $A_{0}$ and $B_{0}$, respectively, whosedomain consists of those elements satisfying an abstract periodic boundarycondition. The motivating example is the derivative on some interval, where theso-defined realisation gives the classical derivative with periodic boundaryconditions. We derive necessary and sufficient conditions for the operatorequality $A^{\#}=-\left(B^{\#}\right)^{\ast}$ and illustrate our findings byapplications to the classical vector analytic operators$\mathrm{grad},\,\mathrm{div}$ and $\mathrm{curl}$. In particular, therealisation $\mathrm{curl}^{\#}$ naturally arises in the study of so-calledBeltrami fields.

A Note on Some Non-Local Boundary Conditions and their Use in Connection with Beltrami Fields