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

j=p+1 zjwj . Then Hn can be viewed as the 2n + 1 dimensional Heisenberg group. Indeed, if n = p + q, Q (z, w) = −ImB (z, w) is the standard symplectic form on <2(p+q) via the identification Ψ : <2(p+q) → Cn given by (1.1) Ψ ( x′, x′′, y′, y′′ ) = ( x′ + iy′, x′′ − iy′′) , x′, y′ ∈ <p;x′′, y′′ ∈ <q. Moreover, Ψ provides a global coordinate system (x, y, t) with x = (x′, x′′) , y = (y′, y′′) . The vector fields Xj = −2yj ∂ ∂t + ∂ ∂xj , Yj = 12xj ∂ ∂t + ∂ ∂yj , j = 1, . . . , n and T = ∂ ∂t form a basis for the Lie algebra hn of Hn. As usual, U (hn) will denote its universal enveloping algebra, which can be identified with the algebra of left invariant differential operators on Hn.

L2spectral decomposition on the Heisenberg group associated to the action of U(p,q)

L²spectral decomposition on the Heisenberg group associated to the action of U(p,q)