摘要:

Let D be a bounded simply connected plane domain and let G(D) be its group of conformal automorphisms with metric. In this paper we solve some problems raiscd by Gaier about G(P). In particular we give conditions under which G(D) is a topological group and a locally compact space. We ascuss me srrucrure of the components of G(D).

ISSN:0278-1077    

DOI:10.1080/17476939208814573

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

The class of Kleinian groups which are extreme with respect to Jorgensen's inequality encompasses continuous families of geometrically finite groups as well as uncountably many geometrically infinite groups, Such groups may be obtained as extensions of the classical modular group.An infinite number of non-isomorphic extreme discrete groups arise this way; some, like the Picard group, are of co-finite volume.Other examples are obtained by extending certain triangle groups.

ISSN:0278-1077    

DOI:10.1080/17476939208814574

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

In this note we extend Pfluger's theorem relating logarithmic capacity and extremal length for closed subsets on the unit disc to closed subsets on quasicircles.

ISSN:0278-1077    

DOI:10.1080/17476939208814575

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

In this paper we present new results pertaining to sequences of domains that are approximating another. In particular, the main results are:Let E he a separable Banach space, U be a non-empty open subset of E, ρ be a strictly lower semicontinuous function on U such that d(x,∂U)≧ρ(X) for every x∈U. Let Bρ(U) denote the collection of all finite unions of closed ballswith center x ∈U and p<ρ(x); and let Hρ(U) be the algebra of the complex holomorphic functions in U which are bounded in every set of Bρ(U) furnished with the Fréchet topology of the uniform convergence over the elements of Bρ(U).

ISSN:0278-1077    

DOI:10.1080/17476939208814576

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

Some simple representations of the norms in Bergman-Selberg spaces on strips and the right half plane on the complex plane are given. At the same time, analytic extension formulas of functions to the members of the Bergman-Selberg spaces on the strips and the right half plane are established.

ISSN:0278-1077    

DOI:10.1080/17476939208814577

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

By the method of extremal length, three general theorems are proven which find, as corollaries, sharp coefficient bounds for functions univalent in the exterior of the unit disc, with a standard normalization but also assuming a finite number of initial coefficients are zero, which possess aK-quasiconformal extension to a ring subdomain of the unit disc. All extremal functions are exhibited. Similar estimates are found for functions similar to the above but which omit a fixed disc centered at the origin.

ISSN:0278-1077    

DOI:10.1080/17476939208814578

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

For α>0, letK(k,α) denote the class of normalizedk-convex functions defined on the unit disk D. Loosely speaking, this means thatfis univalent and at each point of the boundary off(D) the euclidean curvature is at least k. Note that K(0,1) is the classical familyKof normalized convex functions. Tne familiesK(k,α) are closely related to convex functions of bounded type as introduced by Goodman. Our main result is that the familyK(k,α) is mapped into K by composition with a certain linear fractional transformation- This fact enables us to give a unified treatment of a number of known results for the familiesK(k,α) and convex functions of bounded type and to establish sharp new results by making use of various theorems for the family K. There is an interesting phenomenon concerning extremal functions. There is a single extremal function, which is unique up to rotation, for the sharp upper and lower bounds onand the sharp lower bound on. On the other hand, for the upper bound onthis same function is extremal only when the modulus of z not too close to one.

ISSN:0278-1077    

DOI:10.1080/17476939208814579

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

Suppose thatFis univalent on the open unit diskU, the complement ofF(U) is a convex set andfor z inU. Let n = 1,2,…,s(Fn) denote the set of functions subordinate toFnHs(Fn) the closed convex hull of s(Fn) andHs(Fn) the set of extreme points of Hs(Fn). Let A denote the set of probability measures onWe prove that) As a corollary we prove that the closed convex hull of the set of functions subordinate tois equal to the set.

ISSN:0278-1077    

DOI:10.1080/17476939208814580

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939208814572

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor