摘要:

Let μ(λ):Δ→Δ be a measurable function depending real analytically on λ as element ofL∞(Δ) with μ(0)=0 andbe the quasiconformal homeomorphic solution of the Beltrami differential equation

ISSN:0278-1077    

DOI:10.1080/17476939508814840

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

LetFbe a relatively closed subset of an open setGof the plane. Alice Roth in [10] proved that if a functionfis a uniform limit onFof holomorphic or meromorphic functions onG, it is possible to select the approximating functionsmin such a way that the difference functionfmcan be extended continuously into the boundary ofF. In this paper we consider the more general situation arising when one replaces ∂ƀ by an elliptic operatorp(D) with constant coefficients. We prove that the natural analog of Roth's theorem for the operatorP(D) holds, at least for bounded open setsG. In those cases where one can find an inversion of the domain, preserving the uniform approximation by solutions of the operator, unbounded open sets are allowed too. This hannens whenP(D)=δ andn=2. In this case we improve the main result of Goldstein andOwin [7], removing most oi the unnecessary conditions assumed in their work.

ISSN:0278-1077    

DOI:10.1080/17476939508814841

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

In this paper, we obtain a certain rigidity property for Kleinian groups. This asserts that ifFandG(both non-elementary torsion-free Fuchsian groups) and [FF] = [GG],thenF=G(all equalities are taken in the sense of Möbius transformations). This result is connected to Torelli's theorem (for closed Riemann surfaces) and can be a step in understanding an equivalent for more general type of Riemann surfaces.

ISSN:0278-1077    

DOI:10.1080/17476939508814842

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

A meromorphic functionf, defined in the unit diskDof a complex plane, is called a normal function ifwheref#(z) is the spherical derivativeoff. Furtherfis called a little normal function ifNormal and little normal functions are characterized by using different area integral conditions. Similar criteria for analytic Bloch and little Bloch functions have been given by K. Stroethoff and R.Zhao but as compared with meromorphic case these results have some clear differences.

ISSN:0278-1077    

DOI:10.1080/17476939508814843

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Letgbe an analytic function on the unit diskD. We study the operatoron the Hardy spacesHp. We show thatTgis bounded onHp, 1 ≤p< ∞ it and only ifgε BMOA and compact if and only ifgε VOMA. Further on the Hilbert spaceH2Tgis in the Schattcn ρ-class it and only ifgis in the Besov spaceBp, 1 <p< ∞. A relation ofTgwith integration operators is also discussed.

ISSN:0278-1077    

DOI:10.1080/17476939508814844

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

In the present paper the authors prove a Parseval–Goldstein type theorem involving a Stieitjes-type integral transform, theKtransform, and the Hankel transform. The theorem is then shown to vield a number of new identities involving several well known integral transforms. Using the theorem and its corollaries, a number of interesting infinite integrals of elementary and special functions are presented. Some illustrative examples are also given.

ISSN:0278-1077    

DOI:10.1080/17476939508814845

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Letbe harmonic and univalent in unit diskUClunie and Sheil–Small asked that iffis real on the rea1 axis withis it true thatfis typically real? In this note, we present a counter-example to snow that the answer is negative.

ISSN:0278-1077    

DOI:10.1080/17476939508814846

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

There exist many results generalizing the Theorem of Tumura–Clunie. Concerning a wider class of differential polynomials we will give a new estimate of the characteristic offwhich allows to derive or improve results of Tumura/Clunie, Hayman, Mues, Steinmetz, Toda, Weissenborn, Xin-Hou Hua, Ishizaki and Yi.

ISSN:0278-1077    

DOI:10.1080/17476939508814847

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

摘要:

Letfbe an analytic function in the open unit disk that assumes the values 0 and 1 at least once and an unequal number of rimes in a disk of radius 1 10-5entered at the origin. We prove thatfmust assume the value 0 or 1 elsewhere in the unit disk. This result is motivated by a control engineering design problem which is also presented.

ISSN:0278-1077    

DOI:10.1080/17476939508814848

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476939508814839

出版商:Gordon and Breach Science Publishers    

年代:1995

数据来源: Taylor