摘要:

Given a sequencef1,f2,… of rational functions, there are two obvious ways of forming a sequence of composites, namely the sequences (fn∘ ∘f2∘f1) and (f1∘f2∘fn). If thefjrandom perturbbations of some fixedfboth nonnormal sets associated with these sequences are perturbations of the Julia set off. The first of the above orders has been considered by Fornaess and Sibonv and it has been shown that the (random) Julia sets are of area zero with probability one. We consider the Julia set corresponding to the second order, it turns out that they depend onfalone and are of positive area almost surely.

ISSN:0278-1077    

DOI:10.1080/17476939608814869

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

LetDandD′be two bounded complete Reinhardt domains inand letF:D → D′be a proper holomorphic mapping. We prove that ifDorD′is not a generalized pseudoellipsoid, then there exist two bidiscs δ ⊆Dand δ′ ⊇D′such thatFrestricts to a proper holomorphic mapFδ → δ ′. From this it is deduced that, ifD≠ δFis always of the formF(z1,z2)= (Azmπ(1), Bznπ(2)), where π is a permutation of {1,2}. This fact brings to the complete classification of all proper mans between bounded complete: Reinhardt domains in.

ISSN:0278-1077    

DOI:10.1080/17476939608814870

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939608814871

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

We prove that a formal power series in 1/x, whose coefficients are in a field extension ofQand are algebraically independent overQ, is differentially transcendental (i.e. not differentially algebraic) over this field extension. This is stated without proof in [2]. This result provides a source of functions analytic at ∞ that are not differentially algebraic overR. Such functions are of particular interest, because their germs belong to Hardy fields, but not to the classEof [1]-the intersection of all maximal Hardy fields.

ISSN:0278-1077    

DOI:10.1080/17476939608814872

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

A closed geodesic in a hyperbolic surface with either a short common orthogonal or many self-intersections is uniformly long. We will prove analogous results for immersed geodesic surfaces in hyperbolic 3-manifolds, that the length of common orthogonal admits a universal lower bound, and that the size of self-intersection singularities has a universal upper bound, both depending only on the area of surfaces.

ISSN:0278-1077    

DOI:10.1080/17476939608814873

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In the paper we give some necessary conditions for a mapping to be ak-geodesic in non-convex complex ellipsoids. Using these results we calculate explicitly the Kobavashi metric in the ellipsoids. wherem< ½.

ISSN:0278-1077    

DOI:10.1080/17476939608814874

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

A new variational method for functions with positive real part is proved. The method is simpler than that of M. S. Robertson in that it does not involvef′(z).

ISSN:0278-1077    

DOI:10.1080/17476939608814875

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

Letdenote the Hardy spaces of analytic functions on the unit discLetAdenote the space of all normalized analytic functions on δ andFurther let2F1(a,b;c;z) and1F1(a;c;z) be, respectively, the Gaussian and the confluent hypergeometric functions on δ.Form> 0 and ß > − 1, an operator [Pmßf] acting on the normalized analytic functionfis defined by the Hadamard convolutionThe main aim of this paper is to determine conditions on the parametersa,b,c,ß andmfor whichf∈Rimplies that each of the convolutionsandbelongs toH∞∩FHereH∞denotes the space of all bounded elements inA.

ISSN:0278-1077    

DOI:10.1080/17476939608814876

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939608814868

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor