Cluster Sets - Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge - Kiyoshi Noshiro - Books - Springer-Verlag Berlin and Heidelberg Gm - 9783540025160 - 1960
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Kiyoshi Noshiro
Cluster Sets - Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 2. Folge Softcover Reprint of the Original 1st Ed. 1960 edition

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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.

136 pages, 1 black & white illustrations, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released 1960
ISBN13 9783540025160
Publishers Springer-Verlag Berlin and Heidelberg Gm
Pages 136
Dimensions 155 × 235 × 8 mm   ·   213 g
Language English  

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