摘要:

This paper is motivated by several recent works studying the mappings of various subclasses of analytic functions by means of certain families of integral operators. The present authors investigate conditions under which some of these integral operators would map starlike and convex functions into the Hardy spaceHρ(0 < ρ ≤ ∞) of analytic functions. Some of the main results presented here are also shown to be applicable to certain generalized hypergeometric functions.

ISSN:0278-1077    

DOI:10.1080/17476939208814582

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

Let Ω be a simply connected planar domain whose boundary is sufficiently smooth. Then some isometrical mappings between the Szegö and the Bergman-Selberg spaces on Ω are constructed, and they give the representations of the members in the Bergman-Selberg spaces in terms of members in the Szegö space. Moreover, for a memberfin these analytic function spaces, some properties of the derivative ′ offare examined.

ISSN:0278-1077    

DOI:10.1080/17476939208814583

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

We study the interplay between the solutionsf=u+iv+jwof the generalized Cauchy-Riemann systemand functions of the reduced quaternionic variablez=x+iy+jt.In particular we show that every solutionfof (H),defined in some neighbourhood of the origin, admits a series expansion in terms of the following elementary polynomial solutionswhere the sum ranges over all multi-indices (μ0,μ1,…,μnwith.

ISSN:0278-1077    

DOI:10.1080/17476939208814584

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

We obtain an improved analogue for general measures of Aleksandrov's theorem concerning the prescription of the radial limits of functions in the Smirnov class on the ball. Considering general measures, we replace the radial limits by the radial maximal functions. We also give an application concerning the canonical factorization of functions in a certain algebra contained in the Smirnov class on the disk.

ISSN:0278-1077    

DOI:10.1080/17476939208814585

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

W. Bergweiler proved in 1990 that the equationf∘g=Qhas infinitely many solutions in the complex plane, providedfand g are transcendental entire functions andQis a non-constant polynomial. We prove a related result, using standard notations from the Nevanlinna theory: Letfbe a non-linear entire function of finite order of growth, letgbe a transcendental entire function of finite lower order and letQbe a non-constant entire function such thatT(r,Q)=S(r,g). If II denotes the canonical product formed with the zeros off∘gQ, thenT(r,φ) ≠S(r,g). As an immediate consequencef∘g−Qhas infinitely many zeros.

ISSN:0278-1077    

DOI:10.1080/17476939208814586

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

The main point of this paper is to define the multiplicity of zero and to establish Rouché's theorem for holomorphic maps in infinite dimensional complex Banach spaces.

ISSN:0278-1077    

DOI:10.1080/17476939208814587

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

We study the analytic continuation of solutions to Dirichlet's problem with real entire data. The domains we study are quadrature domains, domains bounded by ellipses and domains which are bounded by, loosely speakingk:th roots of ellipses. We give a new proof of the known result (see[1]) that when the domain is bounded by an ellipse the solution extends as a harmonic function to all ofR2. Also, we prove the following new results:

ISSN:0278-1077    

DOI:10.1080/17476939208814588

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

In this paper the classPnof the polynomialswhich are univalent in the unit disk as well as classes of nonunivalent polynomials containingPnare investigated. For |ζ|=1 a retractionRζfromPn+1to the subclass ofPncharacterized byis constructed. With the aid of this retraction it can be proved for some suitable functionals that they take their maximum w.r.t.Pnor evenPn+1in the subclassofPndefined by |an|=1/n. For instance, |am| takes its maximum w.r.t.Pninforn=m+1, n=2m-1andm⩾2.

ISSN:0278-1077    

DOI:10.1080/17476939208814589

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

摘要:

The main open question in the theory of meromorphic functions that share four values is: If two nonconstant meromorphic functions share three values ignoring multiplicities and share a fourth value counting multiplicities, then do the functions necessarily share all four values counting multiplicities? We prove a partial result on this question.

ISSN:0278-1077    

DOI:10.1080/17476939208814590

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939208814591

出版商:Gordon and Breach Science Publishers    

年代:1992

数据来源: Taylor