We study the bases and frames of reproducing kernels in the model subspaces $K_{\Theta }^2=H^2\ominus \Theta H^2$ of the Hardy class $H2$ in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels $k_{{\lambda }_n}\left(z\right)=(1-\overline{\Theta \left({\lambda }_n\right)}\Theta \left(z\right))/(z-{\overline{\lambda }}_n)$ under “small” perturbations of the points ${\lambda }_n$. We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces $K_{\Theta }^2$ and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.

Let $M=G/K$ be a Hermitian symmetric space of the noncompact type and let $\pi$ be a discrete series representation of $G$ holomorphically induced from a unitary character of $K$. Following an idea of Figueroa, Gracia-Bondìa and Vàrilly, we construct a Stratonovich-Weyl correspondence for the triple $(G,\pi ,M)$ by a suitable modification of the Berezin calculus on $M$. We extend the corresponding Berezin transform to a class of functions on $M$ which contains the Berezin symbol of $d\pi \left(X\right)$ for $X$ in the Lie algebra $𝔤$ of $G$. This allows...

We construct and study a Stratonovich-Weyl correspondence for the holomorphic representations of the Jacobi group.