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 $\mathbb C$. 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.
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