摘要:

A Hilbert space proof of C Caratheodory's theorem on angular derivatives is presented.

ISSN:0278-1077    

DOI:10.1080/17476938808814282

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

A well-known theorem of Z. Nehari shows how one can locate the singular points of a functionf(z) given bywherepn(z) is the Legendre polynomial of degreen, by relating them to the singular points of the associated functiong(w) given by. This theorem was later generalized by R. Gilbert to the case where, where Cλn(Z) is the ultraspherical polynomial of degreen. In this paper we show a connection between the theory of generalized Faber expansions and the work of Gilbert and Nehari. In fact, we derive theorem for the generalized Faber expansions from which both Nehar' results follow as special cases.

ISSN:0278-1077    

DOI:10.1080/17476938808814283

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938808814284

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

It is shown that the second order differential equationwhere L is rational, has a non-rational meromorphic solutionw=win the plane only ifw(z)is also a solution of some Riccati equationwith rational coefficients or of an equation=n=2, 3.4 or 6. In this caseandrespectively.

ISSN:0278-1077    

DOI:10.1080/17476938808814285

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

We give two kinds of metric conditions on the total cluster set of a bounded analytic function ƒ in the unit disc that, together with its local connectivity imply that ƒ has a continuous extension up to the boundary. This generalizes classical results about continuous extensions of conformal maps.

ISSN:0278-1077    

DOI:10.1080/17476938808814286

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

It is proved that ifƒ =u+iv is analytic in the unit disc Δ and 0 < ρ <1, thenThis inequality is applied to generalize some results of Hardy and Littlewood on ρ-th mean values of harmonic conjugatesuandv

ISSN:0278-1077    

DOI:10.1080/17476938808814287

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938808814288

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

摘要:

Forthe functional Reis maximized over the customary classSof schlicht functionsby exactly two functions which are related by the rotationf(z)→ −f(−z). Each functionfadmissible for some quadratic differential

ISSN:0278-1077    

DOI:10.1080/17476938808814289

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938808814281

出版商:Gordon and Breach Science Publishers    

年代:1988

数据来源: Taylor