## Factorization of functions in generalized Nevanlinna classes

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- by Charles Horowitz PDF
- Proc. Amer. Math. Soc.
**127**(1999), 745-751 Request permission

## 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.## References

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## Additional Information

**Charles Horowitz**- Affiliation: Department of Mathematics, Bar-Ilan University, Ramat-Gan, Israel
- Email: horowitz@macs.biu.ac.il
- Received by editor(s): June 12, 1997
- Communicated by: Theodore W. Gamelin
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**127**(1999), 745-751 - MSC (1991): Primary 30D50
- DOI: https://doi.org/10.1090/S0002-9939-99-04581-5
- MathSciNet review: 1469410