Holomorphic factorization of polynomials

Abstract

We give necessary and sufficient conditions for a holomorphic factorization of an irreducible polynomial P(s, λ), s ∈ Cn, λ ∈ C, in a domain Ω ⊂ Cn which is connected with the ordering of the real part of the roots of the equation P(s, λ) = 0, s ∈ Ω.