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 $\pi_{\alpha}$ be a holomorphic discrete series representation of aconnected semi-simple Lie group $G$ with finite center, acting on a weightedBergman space $A^2_{\alpha} (\Omega)$ on a bounded symmetric domain $\Omega$,of formal dimension $d_{\pi_{\alpha}} > 0$. It is shown that if the Bergmankernel $k^{(\alpha)}_z$ is a cyclic vector for the restriction $\pi_{\alpha}|_{\Gamma}$ to a lattice $\Gamma \leq G$ (resp. $(\pi_{\alpha} (\gamma)k^{(\alpha)}_z)_{\gamma \in \Gamma}$ is a frame for $A^2_{\alpha}(\Omega)$),then $\mathrm{vol}(G/\Gamma) d_{\pi_{\alpha}} \leq |\Gamma_z|^{-1}$. Theestimate $\mathrm{vol}(G/\Gamma) d_{\pi_{\alpha}} \geq |\Gamma_z|^{-1}$ holdsfor $k^{(\alpha)}_z$ being a $p_z$-separating vector (resp. $(\pi_{\alpha}(\gamma) k^{(\alpha)}_z)_{\gamma \in \Gamma / \Gamma_z}$ being a Riesz sequencein $A^2_{\alpha} (\Omega)$). These estimates improve on general densitytheorems for restricted discrete series through the dependence on thestabilizers, while recovering in part sharp results for $G = \mathrm{PSU}(1,1)$.

Density conditions with stabilizers for lattice orbits of Bergman kernels on bounded symmetric domains