摘要:

Diese Arbeit ist Herrn Professor Karl Wilhelm Bauer und Herrn Professor Helmut Florian aus Anlassihres sechzigsten Geburstags gewidmet.

ISSN:0278-1077    

DOI:10.1080/17476938908814333

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938908814334

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

In this paper, the Riemann—Hilbert boundary value problems for overdetermined partial differential equations of first order are considered. Under suitable hypotheses, by using some integral formulae, we get the necessary and sufficient conditions for the solvability of the problem and the explicit formulae of the solutions. It is noticed that there are a lot of differences between the problems for several complex variables and the problems for one complex variable.

ISSN:0278-1077    

DOI:10.1080/17476938908814335

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938908814336

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

LetS1be the boundary of the open unit diskDand letbe the barycentric extension of the sense-preserving homeomorphism. We prove thathas an angular derivative at any boundary point wherehas a non-zero derivative. The proof depends on characterizing certain differentiability properties ofandin terms of their behavior under composition with certain conformal automorphisms ofD.

ISSN:0278-1077    

DOI:10.1080/17476938908814337

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

LetUdenote the set of all Schwarzian derivatives S(f) of holomorphic univalent functionsfin the unitdiskD, We show that if S(f) is a local extreme point ofUthenfcannot omit an open set. The proof uses subordination. We also show that if S(f)∈Uis an extreme point of the closed convex hull coUofU. thenfcannot omit a set of positive area. The proof of this uses Nguyen's theorem on holomorphic Lipschitz functions.

ISSN:0278-1077    

DOI:10.1080/17476938908814338

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

Some refinements of estimates for the coefficients of the Taylor series are studied in Clifford analysis. An explicit estimate for the partial derivatives of Cauchy's kernel is given. With this result Cauchy's estimate for the partial derivatives of a monogenic function is obtained. These are generalizations of those in complex analysis. Moreover a similar explicit estimate for the partial derivatives of a harmonic function is also obtained.

ISSN:0278-1077    

DOI:10.1080/17476938908814339

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

In this paper we establish a plane wave integral representation for monogenic functions in convex compactsets ofwhich refines the representation theorem of Cauchy for such functions. Using this representation, we determine the maximal subset of the unit ball, in which the multiple Taylor series of a left monogenic function in the unit ball converges. In this way an improvement is obtained of results byW K Hayman (see [3]) and K. Sano (see [6])

ISSN:0278-1077    

DOI:10.1080/17476938908814340

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

Let al, ⃛ anbe distinct real numbers mod 2φ and letKbe a closed subset of [0, 1]. Define Ω to be the unit diskDfrom which the slitseiaK, j = 1 …nhave been removed, and letube the harmonic measure of∂Drelative to Ωet letrbe the corresponding harmonic measure when the a, are changed toIn case Ω is simply connected Dubinin has proved thatIn caseBaernstein has proved the stronger result that lor every increasing convex functionand everywe have the integral mean inequality

ISSN:0278-1077    

DOI:10.1080/17476938908814341

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor

摘要:

The paper concerns correlations between boundary value problems and extremal problems for holomorphic functions. Relations to classical topics of function theory are discussed.

ISSN:0278-1077    

DOI:10.1080/17476938908814342

出版商:Gordon and Breach Science Publishers    

年代:1989

数据来源: Taylor