Local holomorphic mappings respecting homogeneous subspaces on rational homogeneous spaces

Localization operators on homogeneous spaces

Let $G$ be a locally compact group, $H$ be a compact subgroup of $G$ and $varpi$ be a representation of the homogeneous space $G/H$ on a Hilbert space $mathcal H$. For $psi in L^p(G/H), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $L_{psi,zeta} $ on $mathcal H$ and we show that it is a bounded operator. Moreover, we prove that the localizat...

Homogeneous Operators on Hilbert Spaces of Holomorphic Functions – I

In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are homogeneous with respect to the action of the Möbius group consisting of bi-holomorphic automorphisms of the unit disc D. For every m ∈ N we have a family of operators depending on m+1 positive real parameters. The kernel function is calculated explicitly. It is proved that each o...

Frames and Homogeneous Spaces

Let be a locally compact non?abelian group and be a compact subgroup of also let be a ?invariant measure on the homogeneous space . In this article, we extend the linear operator as a bounded surjective linear operator for all ?spaces with . As an application of this extension, we show that each frame for determines a frame for and each frame for arises from a frame in via...

Convolution and Homogeneous Spaces

Homogeneous holomorphic hermitian principal bundles over hermitian symmetric spaces

We give a complete characterization of invariant integrable complex structures on principal bundles defined over hermitian symmetric spaces, using the Jordan algebraic approach for the curvature computations. In view of possible generalizations, the general setup of invariant holomorphic principal fibre bundles is described in a systematic way.