H-transformations and their applications to families of univalent and multivalent functions.

H 变换及其在单价和多价函数族中的应用。

基本信息

批准号：
16540178
负责人：
SAIGO Megumi
金额：
$ 1.73万
依托单位：
Fukuoka University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2005
项目状态：
已结题

项目摘要

In this project we focused our attention upon the research to find the various properties about the H-transformations and their applications. H-transformations are integral transformations defined by H-functions. Saigo attempted his main efforts to describing the various properties such as mappingness, boundedness, surjectivity, range and inverse transformations as the mapping acting on various function spaces, from the view point of that the H-transformations can be understood as the generalization of the hypergeometric functions. He also developed several variations of H-transformations and integral transformations related with it. Subsequently, he succeeded the systematic calculation of fractional integrals for the integral transformations with the kernels defined by the product of H-functions of several variables.Owa defined the families of univalent functions which generalise the star-shaped functions and convex-type functions. These families are defined from the view point from that the notions of the basic star-shaped functions and convex-type functions are based on the analyticity of the univalent functions. He found the various properties of inclusions and estimates of the coefficients of the functions.Saito found a new inequality about the coefficients for arguments of some family of analytic functions. Yoshida concerned with Frenkel's lemma associated with an infinite dimensional space. Fukushima was interested in analytic continuation problems for multi-harmonic mappings.

在这个项目中，我们将注意力集中在研究上，以找到有关H-转化及其应用的各种属性。 H-转化是由H功能定义的积分转换。 Saigo试图描述各种属性，例如作用于各种函数空间的映射，从而将H-Transyformations可以理解为超几何函数的概括，以描述作用于各种功能空间的映射，以描述诸如作用于各种函数空间的映射。他还开发了与之相关的H-转化和积分转换的几种变体。随后，他成功地将积分转换的分数积分进行了系统的计算，并通过多个变量的H功能的乘积定义的内核定义了概括星形函数和CONVEX-TYPE函数的函数的家族。这些家族的定义是根据基本星形函数和凸型函数的概念基于单价函数的分析性的定义。他发现了包含物的各种特性和功能系数的估计值。Saito发现了一些分析功能家族的参数系数的新不平等。 Yoshida与Frenkel的引理有关，与无限的尺寸空间相关。福岛对多谐波映射的分析延续问题感兴趣。