ISSN:0278-1077    

DOI:10.1080/17476938408814057

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938408814059

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

In the following we present three theorems on the univalence of a function that is defined in an implicit way. The theorems are independent, but we decided to put them together. because the idea behind the proofs of these theorems is the same.

ISSN:0278-1077    

DOI:10.1080/17476938408814060

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

We discuss various properties of functionsfinLp(—π,π) whose Fourier coefficients vanish off a set. Two types of theorems are proved. The first gives certain implicit conditions onEso that certain functionsFwhich “majorize”falso belong toLp. The second deals with certain specific setsEwhich are lacunary on the negative integers. FunctionsfinLpwhose Fourier coefficients vanish offEbehave likeHpfunctions in several ways. Various open questions are raised.

ISSN:0278-1077    

DOI:10.1080/17476938408814061

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

ISSN:0278-1077    

DOI:10.1080/17476938408814062

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Extremal problems are considered for the class of functions inSthat are Möbius transformations of convex mappings. A variational method based on Julia's formula is used to describe extremal functions for a certain class of problems. These admissible problems are shown to have extremal functions which are either half-plane mappings or Möbius transformations of strip mappings. An explicit solution is given for the second-coefficient problem.

ISSN:0278-1077    

DOI:10.1080/17476938408814063

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

The support points of the classSof univalent functions are preserved under an operation of truncation of the omitted arc. Under the reverse operation of arc extension, these support points are classified as terminal or nonterminal. It is shown that each functional of evaluation at a point ζ in the disk generates a nonterminal support point unless ζ lies on the segment −1 < ζ < (1 −e)/(1 +e). The dynamics of the truncation operation is fully described for point-evaluation functionals by means of the Loewner differential equation. In addition, some general observations are made concerning the truncation process.

ISSN:0278-1077    

DOI:10.1080/17476938408814064

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

There are five sections in this survey paper. In section 1, we indicate why multiplier problems are of some interest. In section 2, we discuss the phenomenon that two distinct spaces of functions can have the same multipliers and relate this to a type of reflexivity. In section 3, we give a concise summary of known results on multipliers ofHpand related spaces. In section 4, we consider the problem of effectively describing multipliers instead of simply characterizing multipliers abstractly. The fifth and final section closes with a list of open problems.

ISSN:0278-1077    

DOI:10.1080/17476938408814065

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Tests are described for determining whether certain functions are the boundary values of analytic functions taking the upper half plane into itself. In one theorem the functions are real-valued and defined on an open interval and a single point. In other theorems, the functions are defined on a real interval taking values in an arc γ in the upper half plane. In every case these results are closely related to Loewner's theorem in which the putative boundary values are required to be real-valued. As in Loewner's theory, the quadratic inequalities are finite sums involving at most the value of the function and its first derivative at points. These results are closely related to the Pick-Nevanlinna inequalities for functions defined on a sequence of points in the upper half plane; the Pick-Nevanlinna inequalities characterize those functions that are restrictions of analytic functions taking the upper half plane into itself.

ISSN:0278-1077    

DOI:10.1080/17476938408814066

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor

摘要:

Letand letIt is shown in particular that, if ƒ has Hadamard gaps, i.e. ifthen there existand curvessuch thatwhere μ cannot be replaced by a faster growing function. If ƒ does not have Hadamard gaps thencan be bounded on a radius.

ISSN:0278-1077    

DOI:10.1080/17476938408814067

出版商:Gordon and Breach Science Publishers    

年代:1984

数据来源: Taylor