摘要:

The Riemann-Hilbert boundary value problem for a holomorphic function in the polydomain and in the unit ball ofis considered. In contrast to well known results in the case of a single complex variable for polydomain the cokernel of the problem turns to have always infinite dimension, while its kernel has the finite dimension. One of the features of the problem for the unit ball is that its boundary coefficient doesn't produce an index.

ISSN:0278-1077    

DOI:10.1080/17476939608814897

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In this article we prove the Cauchy–Kowalewski theorem for the initial-value problemin the spacePD(E) of pseudoholomorphic functions in the sense of Bers.

ISSN:0278-1077    

DOI:10.1080/17476939608814898

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

We describe the iterative behavior of Moebius transformations with values in the quaternions. A classification of the main conjugacy classes is given. The dynamics turns out to be similar to the complex case, with the exception of the case of a two dimensional fixed point manifold. For Moebius transformations mapping the unit ball onto itself an analogue to a theorem of Denjoy–Wolff holds.

ISSN:0278-1077    

DOI:10.1080/17476939608814899

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

As it is well-known, the complex differentiation of a holomorphic function can be inverted by a complex line integral not depending on the path of integration locally, at least. In the present paper inverse integral operators to more general first order operators (containing a partial complex derivative) are constructed. The construction is based on the concept of associated differential operators.

ISSN:0278-1077    

DOI:10.1080/17476939608814900

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In this paper we proved that the Chern numbers of a compact complex manifold covered by a bounded domain have to satisfy certain conditions. For instance, for a compact complex two-fold covered by a bounded domain inthe Chern number21–2must be non-negative, wherec1=1st Chern classC2=2nd Chern class. Some corresponding inequalities for higher dimensional case are also true.

ISSN:0278-1077    

DOI:10.1080/17476939608814901

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

LetH(X,Y)(C(XL,Y)) represent the family of holomorphic (continuous) maps from the complex (topological) spaceXto the complex (topological) spaceY, and letY+=Y∪{∞} be the Alexandroff one-point compactification ofY. We say thatF⊂H(X,Y) is uniformly normal if {fˆ ϕ :fεF, ϕ εH(M,X)} is a relatively compact subset ofC(M,Y+) (with the compact-open topology) for each complex manifoldM. We show that normal maps as defined by authors in various settings are, as singleton sets, uniformly normal families, and prove theorems for uniformly normal families. These theorems include (1) answers to questions posed by Hahn on higher dimensional formulations of classical theorems of Lehto and Virtanen and the Five-Point Criterion of Lappan, and (2) strong forms of Schottky's Theorem proved for and shown to characterize such families of functions. This last result is applied to present a higher dimensional version of a classical lemma of Bohr.

ISSN:0278-1077    

DOI:10.1080/17476939608814902

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

We show that every one parameter holomorphic automorphism group (holomorphic flow) {ψt:tεR} ⊃ Autonwhose time one map ψ1is an affine linear mapis conjugate in AuttoTogether with the results of Ahern and Forstneric [1] this shows thatevery holomorphic flow onwith polynomial time one map is conjugate in Autto a polynomial flow with the same time one map.

ISSN:0278-1077    

DOI:10.1080/17476939608814903

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

I have recently shown that the Bergman kernel associated to a finitely connected domain in the plane is given as an explicit rational combination of finitely many basic functions of one complex variable. In this paper, it is proved that all the basic functions and constants in the new formula for the Bergman kernel can be evaluated using onedimensional integrals and simple linear algebra. In fact, all integrals used in the computations are line integrals over boundary curves; at no point is an integral with respect to area measure required. From a theoretical perspective, these results lead to an understanding of the complexity of the Bergman kernel. From a practical point of view, they give an efficient method to numerically compute the Bergman kernel. Similar results are also proved for the Szego kernel function, the Poisson kernel, and the classical Green's function.

ISSN:0278-1077    

DOI:10.1080/17476939608814904

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

摘要:

In this note we deal with the limit points of zeros of the sections of a power series. The sharpness of Jentzsch's theorem is analysed by constructing a power series with the property that certain subsequences of its partial sums have prescribed sets as their sets of limit points of zeros.

ISSN:0278-1077    

DOI:10.1080/17476939608814905

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939608814896

出版商:Gordon and Breach Science Publishers    

年代:1996

数据来源: Taylor