The zeros of functions in Nevanlinna’s area class

Heilper, A.

doi:10.1007/bf02761820

Cited by 9 publications

(3 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [8] and [9] this was proved for p = 1 and all α. For general p > 1 it follows from the inclusion A p,α ⊂ A 1,α .…”

Section: Charles Horowitzmentioning

confidence: 77%

See 1 more Smart Citation

Factorization of functions in generalized Nevanlinna classes

Horowitz

1999

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

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.

show abstract

“…In [8] and [9] this was proved for p = 1 and all α. For general p > 1 it follows from the inclusion A p,α ⊂ A 1,α .…”

Section: Charles Horowitzmentioning

confidence: 77%

“…The classes A p,α have been considered by several authors (see [4], [5], [6], [8]). In particular, in [6], the authors give a complete description of zero sets for the classes…”

Section: Charles Horowitzmentioning

confidence: 99%

Factorization of functions in generalized Nevanlinna classes

Horowitz

1999

Proc. Amer. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Similar arguments lead to similar assertions. Approximately at the same time after the appearance of [37], G. Heipler and E. Beller provided closely related results in this direction of research (see [3], [4], Area Nevanlinna type classes of analytic functions 73 [17]). We mention also separately [27], where new promising approaches were provided to this classical problem, related with the description of zero sets of analytic Nevanlinna classes in the unit disk.…”

mentioning

confidence: 97%