摘要:

Letf0,g0be prime entire functions andpa prime number.Let.F=zpchampfng0andG=f0ˆzpsuch thatGis pseudo-prime. Then any non-trivial factorizationsF=fˆg orG=fˆg imply.either.f=λˆzporg=λˆzpwith A linear polynomial λ(whenp=2,g0 is also assumed to be non periodic).

ISSN:0278-1077    

DOI:10.1080/17476939608814850

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

Let α ε [0,1]pbe an analytic function in the unit discEqandhbe analytic and univalent functions inE, Φ be an analytic function in a certain domainD⊃q(E). The authors study the differential subordinationsandwherez⊂EExamples of the application of these results are given.

ISSN:0278-1077    

DOI:10.1080/17476939608814851

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

Top-speed holomorphic motions on Riemann surfaces are defined and discussed. The main result here shows that for Riemann surfaces without ideal boundary curves the motion of one point moving at top speed cannot be extended to a motion of the whole surface if one requires the extension to also be a top-speed motion. Curt McMullen had previously shown the same result for compact surfaces with perhaps finitely many punctures.

ISSN:0278-1077    

DOI:10.1080/17476939608814852

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939608814853

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

A generalized Hele-Shaw problem is investigated taking squeczing effects, gap geometry and non-constant injection or suction rate into account. Complex analytic method is applied, the complex velocity potential turns out to satisfy an inhomogenous linear Beltrami equation and hence is related to quasiconformal mapping with a homeomorphism of the Beltrami equation. The inversefof this mapping satisfies a nonlinear partial differental equation in form of a Dirichlet problem on the unit circleS′ Using the Schwarz formula this problem leads to a Cauchy-Kowalevsky kind of problem. An existence, uniquences and regularity result is shown via the Banach Scale method which imply the same result for the free boundary Γ(t):=f(t,S1).

ISSN:0278-1077    

DOI:10.1080/17476939608814854

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

This paper considers the problem oi holomorphic extension of compact families of holomorphic proper mappings between bounded pseudoconvex domains with real analytic boundaries. Some results on the uniform extension are established We prove a general version of Vitushkin's theorem.

ISSN:0278-1077    

DOI:10.1080/17476939608814855

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

G. Jank, E. Mues and L. Volkmann proved that if a nonconstant meromorphic functionfshares a nonzero finite valueaCM (counting multiplicities) with its first two derivativesf′and, thenf≡f′. It is also noted there that this is not the case fora=0. In this note we consider the casea=0 and IM (ignoring multiplicities) under certain andiiional conditions, one of which requires that the third order derivativeshould also share 0 IM withand the other is on the number of the zeros and multiple poles off. We prove that each of the conditions can reducef/f′to possibly a linear polynomial

ISSN:0278-1077    

DOI:10.1080/17476939608814856

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

Using a modified theory of integral operators it is possible to relate radially symmetric, time-dependent parabolic problems in a given number of dimensions to a similar problem in fewer dimensions. This allows to generalise results about analytic solutions, such as the domain of convergence, from the lower dimensional case. As a special case the heat equation is taken. Using the associated integral operator basic solutions can be constructed, which allow a scries development of an analytic solution, converging normally in a maximal radially symmetric domain.

ISSN:0278-1077    

DOI:10.1080/17476939608814857

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In this paper we prove that if 0<p<2 andfis a function analytic in the unit disc δ then, for almost every θ in the set of those θ such thatfhas a non-tangential limit ateiθ. In particular, this holds for almost every θ inRiffis in the Nevanlinna classNand we prove that this result is sharp in a very strong sense. Namely, we prove that if 0<p<2 then given any positive functione(r) defined on[0,1] and tending to 0 asr→ 1 there exists a functionfanalytic in δ and continuous on δ such that, Our results extend to the range 0<p<2 knownresults of zygmundand Hallenbeck and Samotij valid forp= 1.

ISSN:0278-1077    

DOI:10.1080/17476939608814858

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In the Summer Seminar at Tateyama in Japan on Several Complex variables, July l8, 1994, Professor T Ohsawa posed the following problem in his talk [13].

ISSN:0278-1077    

DOI:10.1080/17476939608814859

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor