Cluster Sets

Cluster Sets

Author: Kiyoshi Noshiro

Publisher: Springer Science & Business Media

ISBN: 9783642859281

Category: Mathematics

Page: 136

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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.
Cluster Sets
Language: en
Pages: 136
Authors: Kiyoshi Noshiro
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

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
Restricted Cluster Sets
Language: en
Pages: 10
Authors: Paul Erd©ʼos, George Piranian
Categories: Functions
Type: BOOK - Published: 1960 - Publisher:

Books about Restricted Cluster Sets
The Theory of Cluster Sets
Language: en
Pages: 224
Authors: E. F. Collingwood, A. J. Lohwater
Categories: Mathematics
Type: BOOK - Published: 2004-06-03 - Publisher: Cambridge University Press

An introduction to the theory of cluster sets, a branch of topological analysis.
Cluster Sets of Pseudo-meromorphic Functions
Language: en
Pages: 15
Authors: David Arne Storvick
Categories: Conformal mapping
Type: BOOK - Published: 1961 - Publisher:

Books about Cluster Sets of Pseudo-meromorphic Functions
Radial Cluster Sets and the Distribution of Values of Meromorphic Functions
Language: en
Pages: 33
Authors: William Blauvelet Woolf
Categories: Functions, Meromorphic
Type: BOOK - Published: 1959 - Publisher:

Books about Radial Cluster Sets and the Distribution of Values of Meromorphic Functions