We define the Weyl functional calculus for real and complex symmetric domains, and compute the associated Weyl transform in the rank 1 case.

Let $G$ be the semidirect product $V⋊K$ where $K$ is a semisimple compact connected Lie group acting linearly on a finite-dimensional real vector space $V$. Let $𝒪$ be a coadjoint orbit of $G$ associated by the Kirillov-Kostant method of orbits with a unitary irreducible representation $\pi$ of $G$. We consider the case when the corresponding little group $H$ is the centralizer of a torus of $K$. By dequantizing a suitable realization of $\pi$ on a Hilbert space of functions on ${ℂ}^n$ where $n=dim(K/H)$, we construct a symplectomorphism between...

* The research has been partially supported by Bulgarian Funding Organizations, sponsoring the Algebra Section of the Mathematics Institute, Bulgarian Academy of Sciences, a Contract between the Humboldt Univestit¨at and the University of Sofia, and Grant MM 412 / 94 from the Bulgarian Board of Education and TechnologyThe present survey introduces in some classical properties of the universal coverings of the projective algebraic manifolds. All the results are non-original. A forthcoming note is...

Let ${ℛ}_{\alpha }$ be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by $\alpha \in ℂ$. I give an elementary proof of the necessary and sufficient condition for ${ℛ}_{\alpha }$ to be a locally finite complex measure (= complex Radon measure).