摘要:

It is well known, that the derivative of a holomorphic function can be estimates by the sup-norm of the function itself:In the present paper we investigate the validity of similar estimates for generalized analytic vectors (in the sense of B. W. Bojarski [1]), i.e. solutions of the elliptical systemForq-holomorphic vectors (i.e. in the casee=f=0) we will prove estimates in theC-C∞- andLp-norms by means of a Cauchy-integral representation. The general case can be reduced to the consideration ofq-holomorphic vectors by applying a modifiedT-operator.

ISSN:0278-1077    

DOI:10.1080/17476939408814725

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this paper, we discuss the solvability of certain nth order systems arising from bi-analytic functions

ISSN:0278-1077    

DOI:10.1080/17476939408814726

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this note we present a simple and efficient algorithm to calculate Taylor polynomials of implicit functions, of inverse functions, and of solutions of ordinary differential equations. We give implementations in the Computer Algebra system DERIVE that demonstrate the efficiency of the algorithms in practice.

ISSN:0278-1077    

DOI:10.1080/17476939408814727

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

LetSdenote, as usual, the class of normalized schlicht functions and letFdenote the class of analytic functions in the open unit disk D, having no fixed point there. We prove the following covering theorem: For every functionf.g,fεS,gεF, the image covers at least the open disk

ISSN:0278-1077    

DOI:10.1080/17476939408814728

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

M. Nowak has recently proved that iffεBMOA andf(O) = 0 then there exists a positive constant A which depends only on the BMOA-norm offsuch that forp≥In this paper we prove that this result remains true for 0<p<1.

ISSN:0278-1077    

DOI:10.1080/17476939408814729

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

Properties of homogeneous polynomials which are extreme points of the closed unit ball of the spaceH∞(B) of bounded analytic functions on the open unit ball inCnare studied. A complete characterization is given in the case of degree 2 and applied to the study of holomorphic functions onBhaving positive real part. A sufficient condition for extremality is also given.

ISSN:0278-1077    

DOI:10.1080/17476939408814730

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

In this paper, we define a generalization of the Schwarzian derivative of analytic functions to holomorphic curves in projective spaces, the Schwarzian curvatures. We study the curves with constant Schwarzian curvatures, the curves with prescribed Schwarzian curvatures, the Schwarzian curvatures of a given curve, and the transformation rules for the Schwarzian curvatures under a coordinate change.

ISSN:0278-1077    

DOI:10.1080/17476939408814731

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

摘要:

We study the polar singularities of solutions to quasilinear elliptic equations of the form (a(|Du|)Du)= 0 in the plane. We assume a degenerate (and singular) ellipticity condition which, essentially, says that the equation can be formally transformed into a uniformly elliptic one, when we perform the divergence. Thep–laplacian is included as a special case. We represent the complex gradient ∂zuaround a non–removable polar singularityz0in terms of a series expansion of a quasiconformal mappingH, wherembeing the index ofDuinz0:. The analysis of the asymptotic behavior ofHgives power estimates from above and below for |Dudepending on the ellipticity constants and on the indexm. Moreover, we also obtain an upper bound formdepending on the rate of growth of |Du| atz0. The theory of quasiconformal mappings and the method of the hodograph transformation are used.

ISSN:0278-1077    

DOI:10.1080/17476939408814732

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939408814724

出版商:Gordon and Breach Science Publishers    

年代:1994

数据来源: Taylor