Convergence results for families of univalent mappings on the unit ball in C^n

Abstract

Let e S t (B n ) be the family of normalized univalent mappings on the Euclidean unit ball B n in C n , which have generalized parametric representation with respect to time-dependent operators A ∈ e A, where e A is a family of measurable mappings from (0,∞) into L(C n ) with some particular properties. Also, let e RT(idBn,(NA(t))t∈(T0,T)) be the time-T -reachable family of the control system C((T0,T),(NA(t))t∈(T0,T)), where A ∈ e A and T0 ≥ 0. In this paper we obtain certain convergence results for the families e