turkmath.org

Weighted spaces of holomorphic functions with O- and o-growth conditions play an important role in analysis and its applications. In spite of more than 30 years of eorts, not so many results of complete type have been obtained to characterize their topological properties in terms of weights. In the talk some new results in this direction will be presented. We concentrate on some aspects concerning the projective description problem for weighted (LB)-spaces, mainly on the topological consequences of algebraic equalities between (LB)- spaces with O- and o-growth conditions, as well as their projective hulls. In particular, it will be shown a way how we can completely remove or signicantly weaken some stringent conditions used before in many papers studying similar problems.