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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Denote by G = U(p, q) the orthogonal group of the sesqui-linear quadratic form \({[x,\, y]=x_1\overline y_1 +\cdots x_p\overline y_p -x_{p+1}\overline y_{p+1} -\cdots - x_{p+q}\overline y_{p+q}}\) on \({\mathbb C^{p+q}}\) and let H 1 = U(p − 1, q) be the stabilizer of the first unit vector e 1. Let H 0 = U(1) and set H = H 0 × H 1. Define the character χ  l  of H by \({\chi_l(h)=\chi_l (h_0h_1)=h_0^l\ (h_0\in H_0,\, h_1\in H_1)}\)where \({l\in\mathbb Z}\) . Define the anti-involution σ on G by \({\sigma (g)=\overline g^{-1}}\) . In this note we show that any distribution T on G satisfying T(h 1 gh 2) = χ  l (h 1 h 2) T(g) (g ∈ G; h 1, h 2 ∈ H) is invariant under the anti-involution σ. This result implies that (G,  H 1) is a generalized Gelfand pair.

(U(p, q), U(p − 1, q)) is a generalized Gelfand pair