| Cluster Sets Softcover Repri Edition Contributor(s): Noshiro, Kiyoshi (Author) |
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ISBN: 3540025162 ISBN-13: 9783540025160 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback Published: January 1960 |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Calculus |
| Dewey: 515 |
| Series: Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge |
| Physical Information: 0.31" H x 6.14" W x 9.21" (0.47 lbs) 136 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |