摘要:

This paper considers the nonlinear boundary value problem with positive shift α(τ) for the generalized hyperanalytic functions in the Doughs' sense. The function α(τ) is defined on the boundaryLand is a bijective mapping fromLinto itself, and it maintains its direction. The existence and uniqueness of the solution to this problem are established by using the successive approximation and continuation method.

ISSN:0278-1077    

DOI:10.1080/17476938708814215

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

It is known that for an entire function f ofintothe set of points a with limr-xmf(r,a)=∞ is of logarithmic capacity zero, and conversely given any setEof logarithmic capacity zero inthere exists an entire function f such that limr-xmf(r,a) ≡ ∞ for every aεE, where mf(r,a) denotes the Nevanlinna proximity function of a. In this note we shall generalize these results to a holomorphic mapping ofinto complex projective spacePm(or a holomorphic curve ofintoPm).

ISSN:0278-1077    

DOI:10.1080/17476938708814216

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

We write δt(ε) for the modulus of continuity at t∈Δ of any holomorphic cover of a Riemann surfaceZby the unit disk Δ That modulus is computed in terms of the absolute value metric for Δ and any metric σ a for Z's topology. THEOREM As t goes to the rim of Δ, the rate at which δt(ε) goes to zero satisfies, for each ε the restrictionif and only if every family Hol(X, Z) is σ-equicontinuous {i.e. σ is a metric of equicontinuity for Z). In particular, that rate's dependence on σ satisfies the restrictionwhen σ = dz, the Kobayashi distance (known to be a metric of equicontinuity when Z is hyperbolic). With Z ≡ Δ and σ as the absolute value metric, we also compute the minimum of the moduli at t of all biholomorphisms B of Δ to befor 0<ε<1 That minimum coincides with the moduli at t of thoseBwith |B(t)|= ε/2.

ISSN:0278-1077    

DOI:10.1080/17476938708814217

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Let Aut(Un) denote the automorphism group of the polydisk Unin Cn. u denotes the subgroup of Aut(Un) consisting of linear automorphisms. A subspace Y of C(Tn) is Mobius invariant if [f φ: f;εY, φε Aut(Un)] ⊂Y. (Invariance of Y w.r.t. u (or a single automorphism) is defined similarly.) In this paper, we show that a u-invariant closed subspace C(Tn) is Möbius invariant iff it is invariant w.r.t. an automorphism not in u. We show that there are exactlyMöbius invariant closed subspaces in C(Tn). Similar results are proved forFurther. we find all Möbius invariant closed subspaces of C(T2).

ISSN:0278-1077    

DOI:10.1080/17476938708814218

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Let K⊂Cbe compact and triangular schemes of nodes inKand poles inC\K be specified. We obtain necessary and sufficient conditions on the distribution of the poles and nodes such that every functionfholomorphic onKmay be approximated uniformly onKby a sequence of rational functions with the given poles which interpolate ∫ in the given nodes. We then show that certain point systems known to be well suited in other interpolation problems may be used successfully in our case. Suppose G⊂Cis a multiply connected domain. We then show that those point systems may be employed similarly to define sets of poles inC\G and sets of nodes inGsuch that every function ∫ holomorphic inGis the limit of the associated rational interpolants locally uniformly inG.

ISSN:0278-1077    

DOI:10.1080/17476938708814219

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Pseudo-differential operators on smooth closed curves admit a rather simple representation in terms of Fourier series which became extremely useful in applications. This representation has been given by Agranovich. Here we present an elementary proof.

ISSN:0278-1077    

DOI:10.1080/17476938708814220

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814221

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

In previous work we have defined and studied holomorphic functions in tubeswhich generalize the HardyHρ(TB)spaces; the baseBof the tubeTBis a proper open subset ofIf B=C, an open convex cone inand 1 < ρ ⩽ 2, we have proved that our new functions have distributional boundary values in the strong topology ofpas. In this paper we continue to study these new functions and extend the existence of boundary values to the cases 2 < ρ < ∞ We prove that our functions obtain boundary values in the strong topology ofPas, whereCis a polygonal cone or a regular cone, for the cases 2 < ρ < ∞.

ISSN:0278-1077    

DOI:10.1080/17476938708814222

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814223

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Two theorems on Nielsen cores are proven. The first gives an inequality for the lengths of boundary curves: the second deals with the lengths of curves connecting boundary curves.

ISSN:0278-1077    

DOI:10.1080/17476938708814224

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor