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Proceedings of the American Mathematical Society
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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Additional Information

Charles Horowitz
Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel
Email: horowitz@macs.biu.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04581-5
PII: S 0002-9939(99)04581-5
Received by editor(s): June 12, 1997
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1999 American Mathematical Society