摘要:

It is not difficult to show that ifis an analytic function on the distinguished boundary, and on the diagonal of the polydisk inCn, then it is also analytic in the closed polydisk. This fact is used in order to give a complete solution to a problem implicit in Kim's work and partially solved by him and Wejntrob. In fact we prove: If the equation(where thepfs are analytic in a simply connected Jordan domainDand on its boundary ∂D, then (*) is disconjugate on [Dtilde]

ISSN:0278-1077    

DOI:10.1080/17476938608814141

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor

摘要:

This is an expository paper. Its purpose is to show, in contemporary mathematical language, how to study Möbius transformations in several dimensions as linear fractions

ISSN:0278-1077    

DOI:10.1080/17476938608814142

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor

摘要:

Suppose thatis univalent inClassical results due essentially to Littlewood and Paley assert that an inequalityimpliesprovided a α > ½ In this paper we show that this implication remains true for α ≧.497. In particular, this confirms Szegö's conjecture that coefficients of fourfold symmetric functions satisfy. Tools include Hayman's theorem which asserts that a univalent function cannot be too big at too many different places, and a localized version of an inequality of Clunie and Pommerenke which those authors had used to prove an=(n−.503) for bounded univalentf

ISSN:0278-1077    

DOI:10.1080/17476938608814143

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor

摘要:

We investigate the topological character of a Lemma of Hayman in his study of the asymptoticbehaviour near x of meromorphic functions: it turns out that the local analyticity of the functionscan be replaced by continuity. The main result is that a function f continuous inCeither has x as an asymptotic value or is bounded on a pathgoing to x or is uniformly bounded on a sequence uf closed curves surrounding the origin and receding to x.

ISSN:0278-1077    

DOI:10.1080/17476938608814144

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor

摘要:

A homeomorphismfof a setfof a setis said to be anL-quasiisometry offor alland ifwhenever ∞ ∈E. Nextfis said to have anM-quasiisometric extension toF⊂R2if there exists anM-quasiisometrygofE∪Fsuch that g|E=fSuppose next thatDis a Jordan domain inR2with boundaryCand that ϕ is anL-quasiisometry ofC.This paper contains complete solutions to the following Schoenflies type extension problems.Problem A.Given a domainDfor which quasiisometries ϕ ofCdoes ϕ have a quasiisometric extensiongtoD? Problem B.For which domainsDdoes each quasiisometry ϕ ofChave a quasiisometric extensiongtoD? It turns out that whenC⊂R2, each quasiisometry ϕ ofChas a quasiisometric extension toDif and only ifDis a quasidisk.

ISSN:0278-1077    

DOI:10.1080/17476938608814145

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor

摘要:

We give necessary and sufficient conditions for a simply connected planar domain to have the Poincare inequality hold for functions withL2derivatives on the domain.

ISSN:0278-1077    

DOI:10.1080/17476938608814146

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor

摘要:

Associated to a meromorphic quadratic differential with at most simple poles on a Riemann surface R is a singular flat metric. Existence and uniqueness theo~ems for geodesics are estahlished when this metric is rehtricted to the surface R that results from puncturing R at a discrete set of points including the poles. In effect. a generalization of Teichmiiller's Lemma is required.

ISSN:0278-1077    

DOI:10.1080/17476938608814147

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor

摘要:

Bounds on the differences of derivatives are found for functions in S whereis analytic and one-to-one in the unit disk: It is shown that the Kobe function provides the upper bounds on the magnitudes of these differences. The estimates generalize a theorem of Landau.

ISSN:0278-1077    

DOI:10.1080/17476938608814148

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor

摘要:

The phenomenon of nonunique extremality of quasiconformal mappings with specified boundary values is studied by means of the known examplewith the boundary values. The concept of critical extremal mapping is introduced. By constructing an appropriate class of variations ofAkwithin the class of extremal mappings it is shown thatAkis a noncritical extremal for everys, 1 <s< 3. A critical extremal is explicitly identified whens= 2.

ISSN:0278-1077    

DOI:10.1080/17476938608814149

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor

摘要:

We investigate the relations betweenf−1(0) andf−1(1) wherefis an entire transcendental function. Small subsets of the union restrict the rest of these sets. Iffis of finite order, then there are geometric and algebraic relations between these sets.

ISSN:0278-1077    

DOI:10.1080/17476938608814150

出版商:Gordon and Breach Science Publishers    

年代:1986

数据来源: Taylor