ISSN:0278-1077    

DOI:10.1080/17476938208814461

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

Pommerenke initiated the study of linearly invariant families of functions defined in the unit disk D. A holomorphic functionfon D is called linearly invariant if the family of all Koebe transforms offhas finite linear invariant order. A functionfis linearly invariant on D if and only iffis uniformly locally univalent in the hyperbolic sense; that is, there is anr> 0 such thatfis univalent in every hyperbolic disk of radiusr. We present two extensions of the notion of linear invariance to general planar regions, one involves the hyperbolic metric and the other the quasihyperbolic metric. We relate these two concepts of linear invariance to uniform local univalence relative to each of these metrics. For uniformly perfect regions all of these concepts coincide; we obtain various inclusion relations for non-uniformly perfect regions. Finally, we characterize entire functions which are uniformly locally univalent relative to the euclidean metric and establish a curious connection between functions which are not uniformly locally univalent relative to the quasihyperbolic metric on some region and uniformly locally univalent entire functions.

ISSN:0278-1077    

DOI:10.1080/17476938208814462

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

Ifw(z) is an elliptic linear fractional transformation of finite orderp, and the analytic functionsatisfies, we give the form of the continued fractions similar toP-fractions, associated fractions and regularC-fractions for. Three examples are given.

ISSN:0278-1077    

DOI:10.1080/17476938208814463

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

In this paper the general solution of the equation (D − λ)w= 0 inSO(m)-invariant open subsets όmega of Rmis obtained, wherebyDis the Dirac operator and λ is a complex constant. The results thus obtained are used to solve the eigenvalue problem for the Dirac operator corresponding to the half-Dirichlet problem for the unit ball in Rmand to construct the fundamental solution of D − λ and integral representation formulae.

ISSN:0278-1077    

DOI:10.1080/17476938208814464

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

Holomorphic vectors inC2are complex valued vectors with two components arising as a solution of equationwith elliptic first order matrix-valued operator. The Kernel Matrices for holomorphic and antiholomorphic vectors are introduced . By means of Kernel Matrices Different properties of the solutions of first order elliptic system inC2are investigated.

ISSN:0278-1077    

DOI:10.1080/17476938208814465

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

Description of right hand sides from subspaces of the Hilbert space for solvability of inhomogeneous elliptic systems in multiply connected domains with given Cauchy dates on the boundary is given. The Schwarz boundary value problem for general elliptic systems in multiply connected domains by means of the integral equations in domain is investigated.

ISSN:0278-1077    

DOI:10.1080/17476938208814466

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

There are many applications and extensions on the Tumura-Clunie theorem. Generalizing a result of Weissenborn we prove that, for any meromorphic functionf(z) and any differential polynomialP[f] of weight less than n, either the inequalityholds or there exists a small functiona(z) related tof(z) such thatWe also consider the case where the degree of P[f] is less than n.

ISSN:0278-1077    

DOI:10.1080/17476938208814467

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938208814460

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor