摘要:

In a simply-connected domain, two kinds of distances are suggested by the classical theorem of Hardy Littlewood on Hölder classes in a disk. These distances are estimated and compared by conformal mapping, an elementary approximation lemma, and the inequalityfor schlicht functions.

ISSN:0278-1077    

DOI:10.1080/17476938408814086

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Suppose thatgis an inner function in the unit ballBofand thatvis a nonnegative subharmonic function inBthat identifies every pair of points that is identified byg. (Thusvis a function ofgbut nothing is assumed a priori about the nature of this function.) It is proved that (i)ris then plurisubharmonic and (ii) ifrhas a harmonic majorant inB, then the least harmonic majorant ofris pluriharmonic and is a harmonic function ofg. The theorem holds actually for every holomorphicg:that hasg(B)and g(∂B) “almost disjoint”. Among the applications are some that deal with Hardy spaces (the casev=|f|p).

ISSN:0278-1077    

DOI:10.1080/17476938408814087

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

LetDbe the unit disk in. It is shown that ifis any simply connected domain containing a sufficiently large disk, then the radius of univalence of the family {f: log f'(D) ⊂ R} is the same as that of {f: log f' mapsD1 – 1 ontoR}. it is also shown that forMsufficiently large the radius of univalence of {f: |f“(z)/f'(z)|≤MinD} is π/M. In addition, locally extremal functions corresponding to the problem of determining sup{M:|f”(z)/f'(z)|≤MinDimplies thatfis univalent inD} and for the John constant problem for the upper half-plane are identified.

ISSN:0278-1077    

DOI:10.1080/17476938408814088

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Letbe an analytic function such that Im F(0)=0. It is proved thatfor everyt>0. Moreover, the constant π/2 is the best possible in this inequality.

ISSN:0278-1077    

DOI:10.1080/17476938408814089

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

The biregular functions constitute in a certain way an extension to two higher dimensional variablesof the one Clifford-variable monogenic functions. From a Bochner-Martinelli formula forC1-functions in the biregular setting, a Cauchy integral formula with non-biregular kernels is obtained, which allows the investigation of the Taylor series of a biregular function in an open ball of.

ISSN:0278-1077    

DOI:10.1080/17476938408814090

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Let the differential systemwhereDis the diagonal matrixand the elements αij(Z) of

ISSN:0278-1077    

DOI:10.1080/17476938408814091

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938408814092

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Let Ω be a finitely connected closed point set in the complex plane with a piecewise smooth boundary ∂Ω. The approximation of functions analytic on Ω, by rational functions determined by interpolation or least squares approximation at preselected nodes is discussed. Attention is focussed on simple methods for selecting an appropriate rational space and obtaining a fairly well-conditioned rational basis. Applications include the determination of conformal mappings. Numerical examples illustrate the approximation method.

ISSN:0278-1077    

DOI:10.1080/17476938408814093

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Let∑kakznλbe analytic for. It is shown that iffhas Hadamard gaps , i.e.then the finiteness ofessentially equivalent to that ofwhereRis a radius of. More precisely, the sum is finite if the integral is, even for an arbitrary curve instead of a radius with no condition whatever on α. For the other direction the restriction α> –1 is necessary.

ISSN:0278-1077    

DOI:10.1080/17476938408814094

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

The moduli space of plane domains of finite connectivity is described explicitly

ISSN:0278-1077    

DOI:10.1080/17476938408814095

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor