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 $D^{III}_n$ and $\mathscr{S}_n$ be the Cartan domains of type III thatconsist of the symmetric $n \times n$ complex matrices $Z$ that satisfy$Z\overline{Z} < I_n$ and $\mathrm{Im}(Z) > 0$, respectively. For thesedomains, we study weighted Bergman spaces and Toeplitz operators acting onthem. We consider the Abelian groups $\mathbb{T}$, $\mathbb{R}_+$ and$\mathrm{Symm}(n,\mathbb{R})$ (symmetric $n \times n$ real matrices), and theiractions on the Cartan domains of type III. We call the corresponding actionsAbelian Elliptic, Abelian Hyperbolic and Parabolic. The moment maps of thesethree actions are computed and functions of them (moment map symbols) are usedto construct commutative $C^*$-algebras generated by Toeplitz operators. Thisleads to a natural generalization of known results for the unit disk. We alsocompute spectral integral formulas for the Toeplitz operators corresponding tothe Abelian Elliptic and Parabolic cases.

Commuting Toeplitz operators and moment maps on Cartan domains of type III