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多复变Fekete-Szegö问题
On the Fekete-Szegö Problem in Several Complex Variables
令F为单位圆盘上正规化单叶函数族.Fekete和Szegö,证明了如下的著名结果:对λ∈[0,1],成立maxf∈F|a3-λa22|=1+2e-2λ/1-λ.本文研究了Cn中有界星形圆形域上的星形映照的相应问题.定理的证明有假设条件,但该条件在单复变情形下是自动满足的.
Let F be the familiar class of normalized univalent functions in the unit disk.Fekete and Szegö proved the well-known result maxf∈F|a3-λa22|=1+2e-2λ/1-λ for λ∈[0,1].We investigate the corresponding problem for the class of starlike mappings defined on the bounded starlike circular domain in Cn.The proofs of these results use some restrictive assumptions,which in the case of one complex variable are automatically satisfied.
Fekete-Szegö / 问题 / 星形映照 / 有界星形圆形域 {{custom_keyword}} /
Fekete-Szegö / problem / starlike mappings / bounded starlike circular domain {{custom_keyword}} /
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国家自然科学基金资助项目(11261022, 11471111);江西省自然科学重大基金(20152ACB2002)
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