Approximation by Generalized Faber Series in Bergman Spaces on Finite Regions with a Quasiconformal Boundary

AbstractIn this work, for the first time, generalized Faber series for functions in the Bergman spaceA2(G) on finite regions with a quasiconformal boundary are defined, and their convergence on compact subsets ofGand with respect to the norm onA2(G) is investigated. Finally, ifSn(f, z) is thenth partial sum of the generalized Faber series off∈A2(G), the discrepancy ‖f−Sn(f,·)‖A2(G)is evaluated byEn(f, G), the best approximation tofby polynomials of degreen