ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46E10/40, 46A32 Holtmanns, Silke and Bierstedt, Klaus D., Univ. Paderborn, Germany An operator representation for weighted spaces of vector valued holomorphic functions For any weighted space HV (G) of holomorphic functions with a topology stronger than that of uniform convergence on the compact subsets of G and for any quasibarrelled space E we prove the topological isomorphism

HV (G, E′_{b}) = L_{b}(E, HV (G))

and derive a similar, but technically more complicated isomorphism for weighted spaces of continuous functions. This should be compared with the ε-product representation for the corresponding space HV_{0}(G, E) of holomorphic functions with o-growth conditions. We also show

HV_{1}(G_{1}, HV_{2}(G_{2})) = H(V_{1} ⊗ V_{2})(G_{1} × G_{2}).

(The talk will be given by the first-named author.)