Zero distribution for pairs of holomorphic functions with applications to eigenvalue distribution

Abstract

Let f f and g g be holomorphic in an angle Λ \Lambda . Theorem 1 shows that the zero-distributions of f f and g g are comparable if, near ∂ Λ \partial \Lambda , f f and g g grow similarly. This result is applied to analyse the asymptotic behavior of eigenvalues of certain perturbed normal operators.