Algebraic and geometric aspects of rational Γ-inner functions
Algebraic and geometric aspects of rational Γ-inner functions
复制标题
有理 β 内函数的代数和几何方面
DOI：
10.1016/j.aim.2017.12.018
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发表时间：
2018
影响因子：
1.7
通讯作者：
Young, N.J.
中科院分区：
文献类型：
--
作者：
Agler, Jim;Lykova, Zinaida A.;Young, N.J.
集合G= def {（z+ w，z w）：|z| < 1，|W| < 1} G 2具有有趣的复几何性质;它有一个3参数的自同构群，它的边界是一个与莫比乌斯带同胚的直纹曲面，它有一个特殊的子簇，它是G的唯一一个在所有自同构下不变的复测地线。我们利用G的几何学，发展了从单位圆盘到G的闭包Γ的有理映射的一个显式和详细的结构理论，这些有理映射将圆盘的边界映射到Γ的区别边界.
The set G= def {(z+ w, z w):| z|< 1,| w|< 1}⊂ C 2 has intriguing complex-geometric properties; it has a 3-parameter group of automorphisms, its distinguished boundary is a ruled surface homeomorphic to the Möbius band and it has a special subvariety which is the only complex geodesic of G that is invariant under all automorphisms. We exploit the geometry of G to develop an explicit and detailed structure theory for the rational maps from the unit disc to the closure Γ of G that map the boundary of the disc to the distinguished boundary of Γ.