摘要:

LetRi(z) ⃛Rρ(z) be different rational functions and letGbe a domain in. When does there exist a meromorphic map from G into the Riemann sphere which is such that its graph does not intersect any one of the graphsRjj=1,2, ⃛,ρ? This paper gives a partial answer to the question.

ISSN:0278-1077    

DOI:10.1080/17476939508814786

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

A new boundary uniqueness result for holomorphic functions is obtained. Applications are provided.

ISSN:0278-1077    

DOI:10.1080/17476939508814787

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

LetFbe the Fischer space composing of entire functionsfwith finite normsThen, for functionsacomplete condition for the existence ofFfunctionsfsuch thatis given. Furthermore, the approximation offunctions byFfunctions is examined.

ISSN:0278-1077    

DOI:10.1080/17476939508814788

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

We prove the following theorem:

ISSN:0278-1077    

DOI:10.1080/17476939508814789

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Lempert proved that the Kobayashi metric and the Carathéodory metric of smooth strongly convex domains are smooth away from the zero section of the holomorphic tangent bundle. We will show that if the strong convexity is replaced by the weaker condition of strict convexity the above smoothness result is no longer valid even if the boundary is real analytic. We study the smoothness of the Kobayashi metric of ellipsoids. We prove that the Kobayashi metric of domains of the form, wherem≥3/2, is piecewiseC3off the zero section, but notC3.

ISSN:0278-1077    

DOI:10.1080/17476939508814790

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

For A : [0,1] → R real-valued monotone decreasing function on [0,1] satisfying A(l)=0tA(t)→ 0 ast→0+ andtA′(t)/(l−t2) increasing on (0,1), we show thatMA(f) ≥ 0forfclose-to-convex whereThis is analogous to a recent result of Fournier and Ruscheweyh [2]. Analogously we obtain least value ofβso that forganalytic in, the functionsandare convex. Here2F1is the Gaussian hypergeometric function. These results are extended to convexity and order of convexity of convex combinations of the formρz +(1−ρ)F(z)ρ< 1. Corresponding starlikeness results in [2] are also extended to such convex combinations.

ISSN:0278-1077    

DOI:10.1080/17476939508814791

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Sufficient conditions for extending subharmonic and plurisubharmonic functions across a hypersurface are proved. Results of this nature concerning harmonic, pluriharmonic and convex functions are derived.

ISSN:0278-1077    

DOI:10.1080/17476939508814792

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

In this paper we continue with the problem of the existence of entire solutionsFandGto the functional equationwherePandQare given polynomials andHis a polynomial Typically, the results are that, except for certain exceptional cases, the only entire solutionsFandGare polynomial. Often, one can then show, for a particular given pair of polynomialsPandQ, that no polynomial solutionsFandGmay exist. This problem is closely related to the problem of extending harmonically to the entire plane the solution to a Dirichlet problem on an algebraic curve with polynomial boundary data. This paper is closely related to earlier work of Flatto, Newman and Shapiro, Baker and Gross, Flatto, and the present authors.

ISSN:0278-1077    

DOI:10.1080/17476939508814793

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

The primary purpose of this work was to study decompositions of finite Blaschke products. We found that if a finite Blaschke productBcould be written asB∘h=Bwherehis a nontrivial holomorphic function from the unit disk into the unit disk, thenBcould be decomposed into a composition of two finite Blaschke products of lower order. It turns out thathmust be an elliptic Möbius transformation and the decomposition ofBdepends on the cycle decomposition ofhas a permutation. This is the main theorem of the paper. The first proof is classical while the second proof uses hypergroups. The existence of a nontrivial subhypergroup of the hypergroup ofBsay thatBcan be decomposed. The holomorphic functionhis used to establish this subhypergroup. We follow the development of hypergroups by Kenneth B. Stephenson [6] and use analytic continuations to present this theory.

ISSN:0278-1077    

DOI:10.1080/17476939508814794

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

For given complex-valued boundary values one may consider the minimal non-analyticity with which a function having these boundary values can be found. We study the effect of local versus global properties of the boundary values on the minimal non-analyticity.

ISSN:0278-1077    

DOI:10.1080/17476939508814795

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor