摘要:

In this note we consider the stability of theL2-angle between domains in. We prove that if the sequence {Bn} of domains inconverges increasingly to the bounded domainB, andAis a bounded domain in, such that ∂B⊂A, then theL:2-angles γ(A,Bn,) converge to γ(A,B). We give also some generalizations of this result.

ISSN:0278-1077    

DOI:10.1080/17476939308814640

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

In this paper, we will discuss a class of nonlinear boundary value problems for second–order, overdetermined elliptic systems. In particular, we consider the following nonlinear Dirichlet problem:whereG: =G1×G2is a polycylinderGj:={zj:|zj|<|} and ∂G:= ∂G1× ∂G2is its Shilov boundary, ∂Gj:= |zj) = |.

ISSN:0278-1077    

DOI:10.1080/17476939308814641

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

It is proved that the differential equationfor arbitrary ß0, γ0γ1and ß1≠ 0 ±1,±2, -3, -4,… has an entire solution if and only if the condition ß1- 2 - γ2=nin:2+ (ß13)nn= 1,2,… is satisfied. The entire solutionf(x) forn=kk⩾ 1 is of the form

ISSN:0278-1077    

DOI:10.1080/17476939308814642

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

A semigroup generated by two dimensionalCl+αcontracting maps is considered. We call a such semigroup regular if the maximumKof the conformal dilatations of generators, the maximumlof the norms of the derivatives of generators and the smoothness α of the generators satisfy a compatibility conditionK< 1/lα. We prove that the shape of the image of the core of a ball under any element of a regular semigroup is good (bounded geometric distortion like the Koebe 1/4-lemma [1]). And we use it to show a lower and an upper bounds of the Hausdorff dimension of the limit set of a regular semigroup. We also consider a semigroup generated by higher dimensional maps.

ISSN:0278-1077    

DOI:10.1080/17476939308814643

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

In this note, analogues of the Carleson interpolation theorems for the Hardy spaces are proven for Besov spaces and Sobolev spaces of holomorphic functions on the unit disk.

ISSN:0278-1077    

DOI:10.1080/17476939308814644

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

Bounds on differentials and Bessel inequalities are determined for holomorphic maps satisfying Lindelöf's principle inj*-algebras and complex Banach spaces. The cases when superordinate maps are bihoiomorphic with convex ranges or holomorphic linear fractional transformations (in particular, biholomorphic maps which are infinite dimensional generalizations of the classical Cayley, Caratheodory and Möbius transformations) are considered.

ISSN:0278-1077    

DOI:10.1080/17476939308814645

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

In this paper we develop a new method for obtaining Bergman operators with closed-form kernels for equations in two variables. This method results from a combination of the theory of operators of class ε and of operators with rational kernels with Laplace's so-called cascade method. Our method yields an extended class of equations that includes members for which no closed-form kernels were known previously, and it also leads to new kmds of closed-form kernels for equations for which so far only class ϵ operators or operators as developed in [10] were known.

ISSN:0278-1077    

DOI:10.1080/17476939308814646

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

We use ideas from a previous paper by the author to study the analytic continuation of certain domain functions. We present new proofs of some results, which are more or less known, about the Green's function and certain conformal maps of quadrature domains and domains bounded by ellipses. We also obtain some new results about the biharmonic Green's function in quadrature domains.

ISSN:0278-1077    

DOI:10.1080/17476939308814647

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

LetSbe the class of normalized univalent functions. Forand denote the class of such functions byIS.We investigate the range of the functionalsF(z)/zandThe results that we obtain are not sharp, but fairly good for small values ofr.In particular we prove that

ISSN:0278-1077    

DOI:10.1080/17476939308814648

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor

摘要:

In the first part of this note, we consider rigid domains which are invariant under certain elementary groups. Each of them corresponds to an isolated point of the set of Schwarzian derivatives of Schlicht functions in the Banach space of the quadratic differentials. Next, we consider “b-group”, that is, a Kleinian group which has a simply connected invariant component. For finitely generated Kleinian groups, all theb-groups are expected to be in the closures of the Bers embeddings of the Teichmüller spaces. We construct two kinds of counterexamples of this conjecture for infinitely generated Kleinian groups.

ISSN:0278-1077    

DOI:10.1080/17476939308814649

出版商:Gordon and Breach Science Publishers    

年代:1993

数据来源: Taylor