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A factorization result for generalized Nevanlinna functions of the classN k

Authors:

Institution:

(1) Department of Mathematics, P.O. Box 800, 9700 AV Groningen, The Netherlands;(2) Department of Theoretical Physics, State Pedagogical University, 603600 Nizhny Novgorod, Russia;(3) Institut für Analysis und Technische Mathematik, Technische Universität Wien, A-1040 Wien, Austria

Abstract:

LetQ

N _k. It is shown that if agr

is a nonreal pole or a real generalized pole of nonpositive type and beta

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.

Keywords:

ASM Classification Numbers" target="_blank">ASM Classification Numbers 30D50 30E99 47B50

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