Kiyoshi Noshiro

Cluster Sets (eBook, PDF)

• Format: PDF

Produktbeschreibung

For the first systematic investigations of the theory of cluster sets of analytic functions, we are indebted to IVERSEN [1-3J and GROSS [1-3J about forty years ago. Subsequent important contributions before 1940 were made by SEIDEL [1-2J, DOOE [1-4J, CARTWRIGHT [1-3J and BEURLING [1]. The investigations of SEIDEL and BEURLING gave great impetus and interest to Japanese mathematicians; beginning about 1940 some contributions were made to the theory by KUNUGUI [1-3J, IRIE [IJ, TOKI [IJ, TUMURA [1-2J, KAMETANI [1-4J, TsuJI [4J and NOSHIRO [1-4J. Recently, many noteworthy advances have been made by BAGEMIHL, SEIDEL, COLLINGWOOD, CARTWRIGHT, HERVE, LEHTO, LOHWATER, MEIER, OHTSUKA and many other mathematicians. The main purpose of this small book is to give a systematic account on the theory of cluster sets. Chapter I is devoted to some definitions and preliminary discussions. In Chapter II, we treat extensions of classical results on cluster sets to the case of single-valued analytic functions in a general plane domain whose boundary contains a compact set of essential singularities of capacity zero; it is well-known that HALLSTROM [2J and TsuJI [7J extended independently Nevanlinna's theory of meromorphic functions to the case of a compact set of essential singUlarities of logarithmic capacity zero. Here, Ahlfors' theory of covering surfaces plays a funda mental role. Chapter III "is concerned with functions meromorphic in the unit circle.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 136
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642859281
• Artikelnr.: 53099172

Inhaltsangabe

I. Definitions and preliminary discussions.-
1. Definitions of cluster sets.-
2. Some classical theorems.- II. Single-valued analytic functions in general domains.-
1. Compact set of capacity zero and Evans-Selberg's theorem.-
2. Meromorphic functions with a compact set of essential singularities of capacity zero.-
3. Extension of Iversen's theorem on asymptotic values.-
4. Extension of Iversen-Gross-Seidel-Beurling's theorem.-
5. Hervé's theorems.- III. Functions meromorphic in the unit circle.-
1. Functions of class (U) in Seidel's sense.-
2. Boundary theorems of Collingwood and Cartwright.-
3. Baire category and cluster sets.-
4. Boundary behaviour of meromorphic functions.-
5. Meromorphic functions of bounded type and normal meromorphic functions.- IV. Conformal mapping of Riemann surfaces.-
1. Gross' property of covering surfaces.-
2. Iversen's property of covering surfaces.-
3. Boundary theorems on open Riemann surfaces.- Appendix: Cluster sets of pseudo-analytic functions.