Zero sequences of holomorphic functions, representation of meromorphic functions, and harmonic minorants

Let Lambda = {lambda(k)} be a point sequence in a subdomain Omega of the complex plane C. In terms of harmonic measures, Green's functions, balayage, Jensen measures, and so on, general conditions are described ensuring that Lambda is the zero sequence of a holomorphic function in a prescribed weighted space of holomorphic functions in Omega. The question of the representation of a meromorphic function in Omega as the ratio of holomorphic functions without common zeros from a prescribed weighted space is considered in similar terms. Some applications are presented.