摘要:

Univalent logharmonic mappingsfrom the unit disc onto spirallike domains are represented by means of univalent conformal spirallike mappings. Furthermore the class of logharmonic automorphisms onUis completely characterized.

ISSN:0278-1077    

DOI:10.1080/17476938708814256

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Let be distinct real numbers mod 2π andKbe a closed subset of [0,1]. Define Ω to be the unit disk Δ from which the slitsei,aK.j= 1,…n have been removed, and letube the harmonic measure of ∂Δ relative to Ω. Letvbe the corresponding harmonic measure when theaj. are changed toIn case Ω is simply connected Dubinin has proved thatv(0)⩽u(0). It is not known whether this holds in general when Ω is multiply connected. In this paper, we prove it is true when nn⩽ 3. In fact, using*-function arguments, we obtain a much stronger theorem involving integral means.

ISSN:0278-1077    

DOI:10.1080/17476938708814257

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

For a fixed schlicht functionGusing iterations we find necessary and sufficient conditions on the coefficients of a functionfso thatfis subordinate toG. We also show how these iterations may be used to obtain sharp coefficient inequalities for such functions and apply the results to the Krzyż conjecture for 1 ≤n≤ 4.

ISSN:0278-1077    

DOI:10.1080/17476938708814258

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Harmonic mappings arise in several areas of analysis and geometry. Our purpose is to present a general variational method for treating extremal problems over families of univalent harmonic functions which map the unit disk onto a given convex region. In the special case where the target region is again the unit disk, the method leads to sharp estimates for coefficients and other functionals.

ISSN:0278-1077    

DOI:10.1080/17476938708814259

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

In this paper a simplified version is given of the proof of Schiffer's differential equation for univalent functions solving an extremal problem. First an elementary variation of the boundary is made to show without any passage to the limit that it consists of curves satisfying a Lipschitz condition locally. Then the differential equation is obtained by an examination of the limit superior of the difference quotient that avoids the usual appeal to a topological lemma of Haslam Jones.

ISSN:0278-1077    

DOI:10.1080/17476938708814260

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814261

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814262

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

A plane domainGw, symmetric with respect to the originO, is extended by “sector reflections” to a symmetric domain Ğw. A “mapping function” [Wbreve](z) of Ğw(mapping the unit diskGzonto Ğw) is constructed in an elementary way in terms of a mapping functionw(z) ofGwusing essentially the reflection principle. In the case of polygonal domains considered here, the results can be interpreted as relations between Schwarz-Christoffel integrals. This method applies to most domains considered in [2]. where only the ratio of conformal radiiRo(Ğw)/Ro(Gw) was determined. The study of the mapping functions themselves was suggested by Max Schiffer.

ISSN:0278-1077    

DOI:10.1080/17476938708814263

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938708814264

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor

摘要:

Many years ago Friedman [3] determined those functions inSwhich have integral coefficients. Later authors extended this result to the case of functions with coefficients in an imaginary quadratic extension of the rationals [2, 4, 6]. In this paper these results are obtained in a significantly simpler manner and in addition there are found all functions in ∑ whose coefficients are half-integers in an imaginary quadratic extension of the rationals and with constant term zero in their Laurent expansions.

ISSN:0278-1077    

DOI:10.1080/17476938708814265

出版商:Gordon and Breach Science Publishers    

年代:1987

数据来源: Taylor