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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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