Hi, I would like to approximate any 2d conformal mapping, as a sum of elementary conformal mappings. So I would have some basis, a conformal mapping with some parameters, and by adding several ones of those, I would mimic any conformal mapping. I don't know a-prioris the map I'm going to approximate, I just want to be sure that I can approximate all possible conformal maps.
I wonder if such problem have been studied, and I'm not even aware of the keywords that might help me to find the answer. May I have some names, keywords to help me to find what I'm searching for ?
[edit following Omer's answer] the mappings I wish to approximate are isomorphism of a circle, which are bounded. Typically a polygon with straight edges, curved edges...