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On the angular limits of Bloch functions.

Joan J. Carmona, Julià Cufi, Christian Pommerenke (1988)

Publicacions Matemàtiques

This paper contains a method to associate to each function f in the little Bloch space another function f* in the Bloch space in such way that f has a finite angular limit where f* is radially bounded. The idea of the method comes from the theory of lacunary series. An application to conformal mapping from the unit disc to asymptotically Jordan domains is given.

On the approximation of entire functions over Carathéodory domains

Devendra Kumar, Harvir S. Kasana (1994)

Commentationes Mathematicae Universitatis Carolinae

Let D be a Carathéodory domain. For 1 p , let L p ( D ) be the class of all functions f holomorphic in D such that f D , p = [ 1 A D | f ( z ) | p d x d y ] 1 / p < , where A is the area of D . For f L p ( D ) , set E n p ( f ) = inf t π n f - t D , p ; π n consists of all polynomials of degree at most n . In this paper we study the growth of an entire function in terms of approximation...

On the disc theorem

Cabiria Andreian Cazacu (1991)

Annales Polonici Mathematici

Ahlfors' disc theorem for Riemann covering surfaces is extended to normally exhaustible Klein coverings.

On the exceptional set in Nevanlinna's second fundamental theorem in the unit disc.

Arturo Fernández Arias, Francisco Rodríguez Mateos (1996)

Publicacions Matemàtiques

A general example of an analytic function in the unit disc possessing an exceptional set in Nevanlinna’s second fundamental theorem is built. It is used to show that some conditions on the size of the exceptional set are sharp, extending analogous results for meromorphic functions in the plane.

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