摘要:

A classical theorem of Szego states that for functionsunivalent in |z|<1 the sequence of partial sums must be univalent in |z|<1/4. For more general sequences consisting of functions of the form, where {νk} denotes an increasing (finite or infinite) sequence of integers (≧2), we find the radius of univalent. Our work also relates to a recent convoluation conjecture due to Gruenberg, Røming, and Ruscheweyh.

ISSN:0278-1077    

DOI:10.1080/17476939208814506

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

It is shown that permutable rational functions have not only the same Julia set but also the same periodic stable domains. In addition, an extended version of a theorem by Julia is stated.

ISSN:0278-1077    

DOI:10.1080/17476939208814507

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

The following generalization of the Cauchy-Riemann system is being considered. This system, denoted by (H), is closely related to the hyperbolic metric onRn+1+. EmbeddingRn+1+into the Clifford algebra Cn, the powers xk(k∈N) yield solutions of (H). Also, compositions of solution with Möbius transformations inRn+1+lead to solutions of (H). General rules associating new solutions to given ones are finally being investigated.

ISSN:0278-1077    

DOI:10.1080/17476939208814508

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

This paper deals with a special class of integral operators of Bergman type which are applicable to the representation of solutions of linear partial differential equations of second order.

ISSN:0278-1077    

DOI:10.1080/17476939208814509

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

We construct some quadrature domains (q.d.) inR4, andR3from q.d. inR2. We obtain a q.d. inR4by taking a certain symmetric q.d.D⊂R2, and rotating it inR4. For a q.d.D⊂R2whose corresponding distributionThas an order ≥ 1, we show that Ω =D×R1is a q.d. inR3, with distribution equal toT&dx⊗3.

ISSN:0278-1077    

DOI:10.1080/17476939208814510

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939208814511

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

We give an explicit description of the polynomials with the same degree, and the same Julia set, as a given polynomial P, and we determine which of these are conjugate to P. Examples are given of two non-conjugate polynomials which have the same degree and the same Julia set.

ISSN:0278-1077    

DOI:10.1080/17476939208814512

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

In this paper a class of quasiconformal mappingsf=f(z) which are conformal in a neighbourhood of infinity is considered. Besides, their dilatationpis restricted in the mean as in [2], [7], [10] and [11]. For this class an area theorem will be derived which implies the area theorem in [5] and, on the other hand, improves an inequality arising from the solution of an extremal problem for the coefficientαin the series expansionf(z) =z+α1/z+α2/z2+… at infinity. Finally, a generalization connected with other extremal problems is investigated.

ISSN:0278-1077    

DOI:10.1080/17476939208814513

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939208814514

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939208814515

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor