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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Factorization of functions
in generalized Nevanlinna classes

Author: Charles Horowitz
Journal: Proc. Amer. Math. Soc. 127 (1999), 745-751
MSC (1991): Primary 30D50
MathSciNet review: 1469410
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Abstract: For functions in the classical Nevanlinna class analytic projection of $\log |f(e^{i \theta })|$ produces $\log F(z)$ where $F$ is the outer part of $f;$ i.e., this projection factors out the inner part of $f$. We show that if $\log |f(z)|$ is area integrable with respect to certain measures on the disc, then the appropriate analytic projections of $\log |f|$ factor out zeros by dividing $f$ by a natural product which is a disc analogue of the classical Weierstrass product. This result is actually a corollary of a more general theorem of M. Andersson. Our contribution is to give a simple one complex variable proof which accentuates the connection with the Weierstrass product and other canonical objects of complex analysis.

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Charles Horowitz
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel

Received by editor(s): June 12, 1997
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society