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

Let $G$ be a M\'etivier group and let $N$ be any homogeneous norm on $G$. For$\alpha>0$ denote by $w_\alpha$ the function $e^{-N^\alpha}$ and consider theweighted sub-Laplacian $\mathcal{L}^{w_\alpha}$ associated with the Dirichletform $\phi \mapsto \int_{G} |\nabla_\mathcal{H}\phi(y)|^2 w_\alpha(y)\, dy$,where $\nabla_\mathcal{H}$ is the horizontal gradient on $G$. Consider$\mathcal{L}^{w_\alpha}$ with domain $C_c^\infty$. We prove that$\mathcal{L}^{w_\alpha}$ is essentially self-adjoint when $\alpha \geq 1$. Fora particular $N$, which is the norm appearing in $\mathcal{L}$'s fundamentalsolution when $G$ is an H-type group, we prove that $\mathcal{L}^{w_\alpha}$has purely discrete spectrum if and only if $\alpha>2$, thus proving aconjecture of J. Inglis.

Weighted sub-Laplacians on M\'etivier Groups: Essential Self-Adjointness and Spectrum