摘要:

Fatou's Theorem states that a bounded analytic function in the unit disk admits radial limits almost everywhere on the unit circleCIf we relax the condition of boundedness offin the hypothesis of Fatou's theorem to unboundedness of the maximum modulus functionMf(r) such thatMfr<q(r),whereq(r) has a slow growth to ∞ we can only hope to obtain asymptotic values instead of radial limits at points ofC. The MacLane classAof analytic functions is the class of non constant analytic functions in the unit diskDthat have asymptotic values at a dense subset of the unit circleC. The main purpose of this paper is to consider a question posed by MacLane [M2] in 1970 on whether functions inAwith an arc tract have branch points. We answer this question positively in the special cases, where the finite asymptotic values are bounded, or where infinity is linearly accessible at least at two points of the end of the tract

ISSN:0278-1077    

DOI:10.1080/17476939808815081

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

A mistake in [2] is corrected; the mistake was made in an underlying lemma for the ultradistribution boundary value results incontained in [2]. After correcting the mistake we note that the ultradistribution boundary value results remain correct exactly as previously stated. Additionally, future research in this area is indicated and a new lemma which will be a basis for future research is stated.

ISSN:0278-1077    

DOI:10.1080/17476939808815082

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

The purpose of this paper is to present some sufficient conditions in order that biholomorphic automorphism of domain inhas the Poincare recurrence property with respect to the Lebesgue measure

ISSN:0278-1077    

DOI:10.1080/17476939808815083

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

It is shown that every analytic function f(x1,…,xk) defined in the intersection of the complex sphere inCkwith an open bail inCkcan be expanded in spherical harmonics. An application to the theory of Lamé functions is given.

ISSN:0278-1077    

DOI:10.1080/17476939808815084

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

In this paper we establish a boundary behavior theory forHpspaces of Clifford valued functions monogenic in a Lipschitz domain in the case ρ>1 The action of a natural class of integral operators with monogenic kernels is studied on these spaces and several applications to PDE's in non-smooth domains are presented.

ISSN:0278-1077    

DOI:10.1080/17476939808815085

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939808815080

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor