Factorization of functions in generalized Nevanlinna classes

Abstract

Abstract. For functions in the classical Nevanlinna class analytic projection of log |f (e iθ )| 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.