摘要:

This paper is concerned with the spinor systemwhere the mattices, are the generators of the linear irredueihle representation of the Clifford algebra. We investigate the Riemann-Hilbert problem fnr this system, and give a full investigation of this problem in the case of constant coefficients in the boundary condition.

ISSN:0278-1077    

DOI:10.1080/17476939108814488

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

Although the point-to-point reflection principle for harmonic functions vanishing on an analytic surface fails in general inRn, n ≥ 3 except for planes and spheres ([8]), it may still hold for selected points near some surfaces. Here, we establish such reflection about axially symmetric surfaces inR4for poinu on the axis of symmetry.

ISSN:0278-1077    

DOI:10.1080/17476939108814489

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

A higher dimensional version of the classical Littlewood-Paley identity is obtained on the ball. This leads to a characterization of BMOA in terms of Carleson measures as in the setting of the disc.

ISSN:0278-1077    

DOI:10.1080/17476939108814490

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

A holomorphic solution for the Riemann-Hilbert boundary value problem in the Sobolev space Wl, pp(D), 2 <p< ∞, is cnnstrueted. This solution satisfies furthermore prescribed jump conditions on a given finite numbcr of simple smooth non-intersecting closed curves inside the domain D of finite measure. The results are then used to solve a similar prohlem for the more general (linear and nonlinearj complex elliptic partial differential equation.

ISSN:0278-1077    

DOI:10.1080/17476939108814491

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

Let I denote an inner function on the unit disk in the complex plane. Associate with I the star- invariant subspace Kp, (I) of the usual Hardy space Hp, where 1<p<∞. We show that the conditionis equivalent to the continuous imbedding of K2(I) inwhere 0<α<1 and 2≦q≦∞. If q=∞ this reduces to a theorem of Ahern and Clark. Similar embedding theorems are discossed for Kp(1) and Lq(dv) where u is a measure supported on the radius [O, 1].

ISSN:0278-1077    

DOI:10.1080/17476939108814492

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

Letfbe a transeendectal meromorphic function. If we writewhere a0is a small function andthen

ISSN:0278-1077    

DOI:10.1080/17476939108814493

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

Let P denote the set of functions f(z) = i + a1z + a2z2+… that are analytic in the unit disc and satisfy Re f (z)> 0 for |x|< 1. Let Bn={b1, b2,…bn:|bk|< 1, k=1,2,…, n) where n is a natural number, and let P(Bn)={f ∈ P : ak=2bk, k=1,…,n}. We prove that the set of extreme points of P(Bn) consists exactly of the functions of the formwhere.

ISSN:0278-1077    

DOI:10.1080/17476939108814494

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

Letfbe an entire transcendental function and denote the nth iterate offbyfn. Our main result is that if n ≥ 2, then there are infinitely many fixpoints offnwhich are not fixpoints of fk for any k satisfying 1 ≤ k ≤ n. This had been conjectured by I. N. Baker in 1967. Actually, we prove that there are even infinitely many repelling fixpoints with this property. We also give a new proof of a conjecture of E Gross from 1966 which says that if h and g are entire transcendental functions, then the composite function hog has infinitely many fixpoints. We show thath∘g. has even infinitely many repelling fixpoints.

ISSN:0278-1077    

DOI:10.1080/17476939108814495

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

Let t be a complex parameter andwith. Letftbe the normalized quasiconformal mapping wilh complex dilatation μtthat leaves 0.1,∞ fixed. If μtdepends holomorphically on t, then so is ftDespite of this fact, ft1-1does not depend hoiomorphically on t. But we can still derive the first order variational formula ft-1at t=0 with respect to μtprovlded that μt→0 as t→0. Our estimate of thc order of the rernainder term is sharp.

ISSN:0278-1077    

DOI:10.1080/17476939108814496

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor

摘要:

Recently, Mocana [6] has proved that ifis analytic inin, then F(z) is starlike inwhere. In this paper, we will improve the above result.

ISSN:0278-1077    

DOI:10.1080/17476939108814497

出版商:Gordon and Breach Science Publishers    

年代:1991

数据来源: Taylor