摘要:

LetA(X)be the Banach space of integrable, holomorphic, quadratic differentials ϕ on a Riemann surfaceX. We characterize the points ofA(X)at which the norm is weak uniformly convex in terms of the infinitesimal form of Teichmuller's metric onQSmodSand we give a quantified version of this characterization. Sullivan's coiling property applies along any Beltrami line [t|ϕ|/ϕ|] for which ϕ is a point of weak uniform convexity and the amount of coiling is quantified by the quantified version of weak convexity. For a closed setJin, we letA(J)be the Banach space of integrable functions inwhich are holomorphic in the complement ofJ. We generalize Bers' approximation theorem by showing that rational functions with simple poles inJare dense inA(J). Density is with respect to theL1-norm over the whole complex plane, includingJ

ISSN:0278-1077    

DOI:10.1080/17476939608814907

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

The purpose of this paper is to establish a topological isomorphism between the spaceFKof H-hyperfunctions supported by a compactKand the space (G(K))′ of left H-linear functionals onG(K)space of germs of regular functions. The spaceFKis also topologically isomorphic to the spaceR∞1(HP1\K) of left regular functions vanishing at infinity.

ISSN:0278-1077    

DOI:10.1080/17476939608814908

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

This paper deals with initial-regular oblique derivative boundary value problems for nonlinear parabolic complex equations of second order in a multiply connected domain, where coefficients of equations are measurable. We first verify the uniqueness of solution for above problems, and then give a priori estimates of solutions for the problems. Finally, by using the above estimates and the method of parameter extension, the existence of solutions of initial-boundary value problems is proved. The results in this paper are the development of corresponding theorems in [1, 4, 5], here the condition (1.4) is weaker than the corresponding condition in [1, 5], i.e. the constant 4/3 in [1, 5] is replaced by 3/2 in (1.4).

ISSN:0278-1077    

DOI:10.1080/17476939608814909

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In the iteration of transcendental meromorphic functions wandering domains may occur. In this article we discuss the behaviour of the sequence (fn) in a wandering domain. We show that the set of limit functions may consist of any given finite set of constant functions if the constant function ∞ belongs to this set. Furthermore, we show that the set of limit functions can only exist of a finite number of constants if this set is contained in the backward orbit of ∞ or if its elements form an irrationally indifferent cycle which is contained in the Julia set.

ISSN:0278-1077    

DOI:10.1080/17476939608814910

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

Let2F1(a,b;c;z) and Φ(a;c;z) denote the Gaussian hypergeometric function and confluent hypergeometric function respectively. It is well known that iffis univalent in the unit disc δ then the corresponding Alexander transform off, namelydt, is not necessarily univalent in the whole of δ In this paper we determine conditions on the parametersa,bandcso that the Alexander transform, wheref(z)=z2F1(a,b;c;z) or zΦ(a;c;z) is univalent and starlike in the whole of δ. In particular, we obtain conditions ona,b,cto guarantee that2F1(a,b;c;z) (and Φ(a;c;z) resp.) will be univalent in the whole of the unit disc.

ISSN:0278-1077    

DOI:10.1080/17476939608814911

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

We consider systems of formally hyperbolic differential equations in two complex variables and mappings described by differential operators between the solutions of such systems. First we transform these systems to a reduced form and give differential operators of order one. With this we can construct special differential operators of arbitrary order which map holomorphic functions into the set of solutions. As an application we construct a system of differential equations which is in close connection to the iterated differential equation of the generalized axially symmetric potential theory. For this system the Riemann-matrix-function is given also.

ISSN:0278-1077    

DOI:10.1080/17476939608814912

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

Sharp lower and upper bounds and a double inequality expressing quasimultiplicative properties are proved for a distortion function occurring in the study of quasiconformal maps. In addition, we show that our results, combining with a recent result of G. Martin

ISSN:0278-1077    

DOI:10.1080/17476939608814913

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939608814906

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor