The group of diffeomorphisms of the circle: Reproducing kernels and analogs of spherical functions,статья
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Дата последнего поиска статьи во внешних источниках: 12 июля 2017 г.
Аннотация:The group $Diff$ of diffeomorphisms of the circle is an infinite dimensional analog of the real semisimple Lie groups $U(p,q)$, $Sp(2n,R)$, $SO^*(2n)$,
the space $\Xi$
of univalent functions is an analog of the corresponding classical complex Cartan domains. We present explicit formulas for realizations of highest weight representations of $Diff$
in the space of holomorphic functionals on $\Xi$, reproducing kernels on $\Xi$
determining inner products, and expressions ('canonical cocycles') replacing spherical functions.