Homogeneous Operators on Hilbert Spaces of Holomorphic Functions – I
نویسنده
چکیده
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 of these operators is bounded, lies in the Cowen Douglas class of D and is irreducible. These operators are shown to be mutually pairwise unitarily inequivalent.
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