Author | Noshiro, Kiyoshi. author |
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Title | Cluster Sets [electronic resource] / by Kiyoshi Noshiro |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1960 |
Connect to | http://dx.doi.org/10.1007/978-3-642-85928-1 |
Descript | VIII, 136 p. 1 illus. online resource |
I. Definitions and preliminary discussions -- ยง 1. Definitions of cluster sets -- ยง 2. Some classical theorems -- II. Single-valued analytic functions in general domains -- ยง 1. Compact set of capacity zero and Evans-Selbergโs theorem -- ยง 2. Meromorphic functions with a compact set of essential singularities of capacity zero -- ยง 3. Extension of Iversenโs theorem on asymptotic values -- ยง 4. Extension of Iversen-Gross-Seidel-Beurlingโs theorem -- ยง 5. Hervรฉโs theorems -- III. Functions meromorphic in the unit circle -- ยง1. Functions of class (U) in Seidelโs sense -- ยง 2. Boundary theorems of Collingwood and Cartwright -- ยง 3. Baire category and cluster sets -- ยง 4. Boundary behaviour of meromorphic functions -- ยง 5. Meromorphic functions of bounded type and normal meromorphic functions -- IV. Conformal mapping of Riemann surfaces -- ยง 1. Grossโ property of covering surfaces -- ยง 2. Iversenโs property of covering surfaces -- ยง 3. Boundary theorems on open Riemann surfaces -- Appendix: Cluster sets of pseudo-analytic functions