ISSN:0278-1077    

DOI:10.1080/17476939808815121

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Some theorems are proved that generalize the well-known Valiron-Titchmarsh theorem of entire functions.

ISSN:0278-1077    

DOI:10.1080/17476939808815122

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Letfbe a non-Möbius self-map ofC*. WriteJ*(f) for the Julia Set offin Ĉ andJ(f) for the closure ofJ*(f) inČ. Then we have one of the three cases (i)J(f),J*(f) are connected, (ii)J(f) is connected,J*(f) has infinitely many components, (iii)J(f) has two components,J*(f) has infinitely many components. All three cases can occur.

ISSN:0278-1077    

DOI:10.1080/17476939808815123

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

We give a new proof of a generalization of Gol'dberg's theorem that meromorphic solutions of first order algebraic differential equations have finite order of growth. The main tool is a result of Zalcman concerning normal families.

ISSN:0278-1077    

DOI:10.1080/17476939808815124

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

In [19] Scheinberg generalized a celebrated theorem of Carleman by showing that a continous function onRncan be approximated with arbitrary speed by entire ffunctions ofncomplex variables. Alexander showed in [1] that an unbounded smooth curve inCnis such a set of Carleman approximation. Frih and Gauthier in [8] studied Carleman approximation by entire functions inCnon products of curves inCn, n1+…+n>k=n. In the present paper, we show that a product set in a product of Riemann surfaces is a Carleman set if and only of each projection is a Carleman set, thus generalizing the results of [18] and [19].

ISSN:0278-1077    

DOI:10.1080/17476939808815125

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

We consider an entire functionfbounded on every raybut not constant, and define for every complex λ. We show thatG(λ) is holomorphic onCθ if only iffid bounded in a sector θ ε – < argz< θ + ε. OtherwiseGhas singularities at all points ofC:θ.

ISSN:0278-1077    

DOI:10.1080/17476939808815126

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939808815127

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Letfbe a meromorphic function in the plane, denote byA(r, f) the spherical area ofdivided by the area of the Riemann sphere. Fora, ∈CputandPutB(f) = {a : b(a,f) > 0). Asssume that cardB(f) is at most countable, and.

ISSN:0278-1077    

DOI:10.1080/17476939808815128

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939808815129

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

LetGbe a family of functions analytic in a domainDin the complex plane. We prove thatGis a normal family, provided that for eachf∈GE 9, there existsk=k( f )> 1 such

ISSN:0278-1077    

DOI:10.1080/17476939808815130

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor