摘要:

Minimum modulus theorems are important in applications where one has to divide by a given entire function. In this paper, we shall use a very simple and fundamental method to strengthen a theorem of A. Edrei on the minimum modulus of entire functions of order less than one.

ISSN:0278-1077    

DOI:10.1080/17476939608814930

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

Let (xybe the value of the linear functionalyεE*on the elementxεE, whereEis a Banach space with conjugateE*Tbe a unit circumference of a complex plane; and Σ be a a σ-algebra of Borel subsets ofT. Let a functionh:T→E*be strongly measurable and for ∀xεEa functionbe summable. An explicit proof is given that if a set function μσ →>E*, ∀xεE, is a vector measure with a finite total variation, then the function h is Bochner integrable.

ISSN:0278-1077    

DOI:10.1080/17476939608814931

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

A connection between the study of commuting holomorphic maps of the unit disc Δ ofinto itself and the study of holomorphic maps of Δ into itself that belong to the same pseudo-iteration semigroup (in the sense of Cowen) is investigated. The open (and difficult) case in which the maps have derivative 1 at the Wolff point τ ∂ ε Δ is considered in this paper. Among other results, it is proved that the set of all holomorphic maps of the unit disc Δ into itself which commute with a given holomorphic mapfcoincides with the set of all holomorphic maps which belong to the pseudo-iteration semigroup off. The results are obtained under the hypothesis—which appears naturally in the context—that the iterates of the involved maps converge to the (common) Wolff point “non-tangentially”.

ISSN:0278-1077    

DOI:10.1080/17476939608814932

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In this paper, we prove thathas no multiply-connected Fatou components, wheregandhare entire functions, and thereforenon-constant entire) has no Herman rings, which gives a negative answer to Bergweiler's question. Also it is proved thathas no Herman rings, and on the other hand ifhas a multiply-connected Fatou component, then it is necessarily a Herman ring. We also point out thathas no Herman rings if λnis real.

ISSN:0278-1077    

DOI:10.1080/17476939608814933

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

We give a complete description of divisors of entire periodic functions inwith plane zeros.

ISSN:0278-1077    

DOI:10.1080/17476939608814934

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

LetGbe a Fuchsian group. Forzin the hyperbolic plane, denote byD(z) the Dirichlet polygon based atz. We show that the graph {(z,w):wεD(z)} is a pseudoconvex open subset of

ISSN:0278-1077    

DOI:10.1080/17476939608814935

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

Let Z be a sequence of points in the unit disk. For a variety of analytic function spaces, it is shown that the properties of the function

ISSN:0278-1077    

DOI:10.1080/17476939608814936

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

Letbe a region containing the diskfor someR>1, and letfbe a function holomorphic inG. Furthermore, letLn(.;f) denote the Lagrange interpolatory polynomial offin the (n+ 1)st roots of unity. Then it is well-known thatLn(z;f)→f(z) (n→∞) locally uniformly inDR. In [2] and [3] we applied certain matrix summability methods to the sequenceLn(.;f) in order to enlarge the set of convergence. This set is an open set, it depends on the summability method and the singularities off, and it often contains the diskDRas a proper subset. The aim of this paper is to study the rate of convergence.

ISSN:0278-1077    

DOI:10.1080/17476939608814937

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939608814938

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939608814929

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor