ISSN:0278-1077    

DOI:10.1080/17476939008814445

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

We prove an inequality between the area of the omitted set of an analytic functionfand its coefficients. We show that equality holds if and only iffis a univalent function.

ISSN:0278-1077    

DOI:10.1080/17476939008814446

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

We prove the following conjecture, which goes back to Wittich and Frank: letbe a fundamendal system ofwitha1(z) = constaj(z) polynomials (2≦j≦n). If eachwk(1≦k≦n) either has 0 as a Borel exceptional value or is a polynomial, then all the coefficientsaj(z)(2≦j≦n) are constants.

ISSN:0278-1077    

DOI:10.1080/17476939008814447

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

This paper contributes to the theory of quasiextremal distance domains. We present some new properties for these domains and point out results concerning the extension of quasiconformal homeomorphisms.For example, we establish a continuity property for mod(E, F; D) and use this to demonstrate that mod(E, F; D) = cap(E, F; D) wheneverDis a QED domain andE, Fare disjoint compacta in D. Our final result is that if each boundary component of a plane domain is either a point or a Jordan curve and if the domain satisfies a boundary quasiextremal distance property, then there exists a quasiconformal self-homeomorphism of the entire plane which maps the given domain conformally onto a circle domain.

ISSN:0278-1077    

DOI:10.1080/17476939008814448

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

This paper is a continuation of [S]. Here we propose an elementary generalization of the Weierstrass approach to holomorphic function theory into the theory of monogenic functions. The monogenic functions are generated by convergent permutational power series.

ISSN:0278-1077    

DOI:10.1080/17476939008814449

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

An entire functionfis called universal (in the sense of MacLane) if a suitable sequencef(nk)of derivatives offconverges to any preassigned entire function, locally uniformly in the whole plane. We show: Given any functionthere exists a universal functionfsuch that, while there can be no universal function with.

ISSN:0278-1077    

DOI:10.1080/17476939008814450

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939008814451

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

A variational method is developed for a family of normalized Mobius transformations of starlike mappings.It is applied to a class of functionals with the result that extremal functions have an elementary form. As a special case, the radius of starlikeness of this family is determined to be approximately 0.6759.

ISSN:0278-1077    

DOI:10.1080/17476939008814452

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

摘要:

Letk(r) be a general kernel. Relationships between the null sets of LP-capacity Ck.p.and those of Hausdorff measure are studied. The best possibility of the relationships is given by constructing symmetric generalized Cantor sets. Our results generalize [3] and may be considered to be an LP-capacity version of the properties of classical capacitiesCkin Carleson [4,§IV].

ISSN:0278-1077    

DOI:10.1080/17476939008814453

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939008814454

出版商:Gordon and Breach Science Publishers    

年代:1990

数据来源: Taylor