I am not a (complex) analyst but it seems that some of the questions I am working on are related to the following concepts:
- logarithmic capacity
- transfinite diameter
- Green's function of a compact set
- System of Fekete points
- upper regularization
I have looked at various books but some of them are very old (e.g., Hille's Analytic function theory which was published in 1962), and most of them just explain the subject briefly. I am looking for references which are more on the advanced side rather than elementary, to be able to find in them the results I need.