摘要:

We consider several classes of analytic functions with prescribed cluster sets along chosen boundary paths in |z|<R. The construction of such functions is an application of complex approximation theory. We develop a technique for showing that these functions form dense sets of first category in the space of functions analytic in |z|<R. Such functions are thus rare but well dispersed.

ISSN:0278-1077    

DOI:10.1080/17476938908814325

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

It is well known that ifM(z) andN(z) are regular in the unit discU={z:|z|<1} andN(z)mapsUonto a multisheeted domain that is starlike with respect to the origin then Re (M′(z)/N′(z))>β implies Re(M(z)/N(z))>β. In this paper we give a sufficient condition onN(z) which can guarantee that Re(M(z)/N(z))>β′>β. A few interesting applications of this result are also given.

ISSN:0278-1077    

DOI:10.1080/17476938908814326

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

In this work we find the largest domain in which a fixed family of Čakalov-Distler sums is completely multivalent of orderp.

ISSN:0278-1077    

DOI:10.1080/17476938908814327

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

Letbe a univalent mapping of the unit disk (suitably normalized) onto a strip. We prove that the analytic completion ofu,is the Cauihy trdnsiorm of a mcasure on the unii circle. It is also proven that if the range of such anfis starlike then the functionsare are convex in the direction of the imaginary axis for every φ.

ISSN:0278-1077    

DOI:10.1080/17476938908814328

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

Lets(F) denote the set of functions subordinate to a functionFanalytic in the open unit disk Δ. Letbe the set of functionsfanalytic in Δ such thatwhere ∞s(f)denotes the closed convex hull ofs(f). Letdenote those functions analytic in Δ such that the set of support points ofs(f) is. In this paper we investigate the problems of describing functions inandRecently, Abu-Muhanna showed that univalent functions, withconvex and satisfying a smoothness condition at ∞ must be in. We show that: is closed in the space of analytic functions. Consequently anyFunivalent withconvex is in Moreover if such anFis not a half-plane mapping it belongs to

ISSN:0278-1077    

DOI:10.1080/17476938908814329

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

We consider the classB(w0) of bounded analytic functionswin the closed unit disc withw(0)=w0andw(1)=eiθ. Our main result is the determination of the variability region. As an application we prove that the set of normalized univalent functionscontains only starlike functions if and only if.

ISSN:0278-1077    

DOI:10.1080/17476938908814330

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

Holomorphic functions in tubeswhich generalize the HardyHpfunctions are shown to have boundary values on the topological boundaryof the tube. The boundary values are obtained restrictedly and unrestrictedly inL2and in the strong topology of the distribution space ′rther⩾1 the Fourier transform space of the distributions of exponential growth.ℋ′r.

ISSN:0278-1077    

DOI:10.1080/17476938908814331

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938908814324

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor