A factorization result for generalized Nevanlinna functions of the classNk

AbstractLetQ∈Nk. It is shown that if α is a nonreal pole or a real generalized pole of nonpositive type and β is a nonreal zero or a real generalized zero of nonpositive type of the functionQ then the function $$Q_1 (z): = \frac{{(z - \alpha )(z - \bar \alpha )}}{{(z - \beta )(z - \bar \beta )}}Q(z)$$ belongs to the classNk−1.