摘要:

In Analogie zur Darstellung der LösungHfder ersten Randwertaufgabe der Potentialtheorie Hj(z)=∫fdω in einem Gebietgzu der stetigen Funktionfwird die Darstellung der Lösunguder zweiten Randwertaufgabe in der Form u(z)=∫H(.z)dμ gesehen. bei der μ das Maß auf dem Rand vongist. dessen Dichte bezüglich dem Lebesgue-Maß die Normalableitung vonuist.

ISSN:0278-1077    

DOI:10.1080/17476938808814304

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

Iffis a bounded univalent function in the unit diskDwith a K-quasiconformal extension to the plane. then it is known thatfsatisfies a Hölder condition of the form |f(z2)−f(z1)|⩽M|z2−z1|1−k(z1,z2∈Dwhere k=(K−1)/(K+1). For two different normalizalions estimates of the Hölder constantMare given such thatMtends to 1 asKtends to 1.

ISSN:0278-1077    

DOI:10.1080/17476938808814305

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

SupposeGis a bounded domain inRnsuch that the complement ofGsatisfies a capacity dcnsity condition. It is shown that all elliptic measures inGhave a support setwithMoreover, the capacity density condition cannot be removed.

ISSN:0278-1077    

DOI:10.1080/17476938808814306

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

Two algorithms are introduced and shown to lead to a unique product represenatation for a given formal power series 4 with constant term 1. as a product of termswhere theanare polynomials. The degree of approximation by the rational function which is theNth partial product of such terms forn≤Nis investigated. The type of product corresponding to an initial rational functionAis also characterized, as well as the product in some other explicit cases.

ISSN:0278-1077    

DOI:10.1080/17476938808814307

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

We describe the maximal sets Ωnin a circular domain Ω (interior or exterior of a disk) which can actually belong to the imageP(D) of a polynomial of degree n in the unit disk, value in the origin fixed, ifP(D)⊂Ω. We see that there is essentially only one simple family of external polynomials for these situations. Applications include a new sharp univalence criterion for polynomials inD.

ISSN:0278-1077    

DOI:10.1080/17476938808814308

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

In this paper, we investigate the distribution of zeros of solutions of

ISSN:0278-1077    

DOI:10.1080/17476938808814309

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

LetDbe a tempered distribution on the real lineRThe problem of determining all tempered distributionsEonRwith |Ecirc;|=|[Dcirc]| is studied for distributions with compact support If there existsA.Btempered distributions with compact support such thatD=A*Band E=A*B*then |Ê|=|[Dcirc]|, however, it is shown that there are smooth functionsD. Ewith compact support such that |Ê|=|[Dcirc]|, but for which there is no such factorization. This requires having some knowledge of the distribution of the zeros of [Dcirc]: and partly to this end, generalizations of theorems of Titchmarsh on the distribution of the zeros of a Fourier transform are proved.

ISSN:0278-1077    

DOI:10.1080/17476938808814310

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938808814311

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938808814312

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

LetC(β),β ⩾ 0, denote the family of normalized close-to-convex functions of order β. For β=1 this is the usual set of close-to-convex functions, which had been defined by Kaplan.

ISSN:0278-1077    

DOI:10.1080/17476938808814313

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor