Abstract. We first find linear fractional solutions to Abel--Schröder functional equations in Hilbert spaces and then use our results and spiral-like mappings to study the Koenigs embedding property for certain linear fractional transformations.

AMS Subject Classification (1991): 30C45, 46G20, 47A60, 47H06, 47H20

Received October 17, 2001, and in final form August 14, 2002. (Registered under 2885/2009.)