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Cluster Sets by Kiyoshi Noshiro

Cluster Sets

by Kiyoshi Noshiro
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Book cover type: Paperback
  • ISBN13: 9783540025160
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 136
  • Original Price: EUR 49.99
  • Language: English
  • Edition: Softcover Repri
  • Item Weight: 228 grams
  • BISAC Subject(s): Mathematical Analysis and Calculus

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.

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