, Volume 36, Issue 1, pp 121-125

A factorization result for generalized Nevanlinna functions of the classN k

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Abstract

LetQN k. 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 classN k−1.