Author: A. J. Lohwater
Publisher:
ISBN:
Category : Analytic functions
Languages : en
Pages : 24

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Author: E. F. Collingwood
Publisher: Cambridge University Press
ISBN: 9780521604819
Category : Mathematics
Languages : en
Pages : 228

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An introduction to the theory of cluster sets, a branch of topological analysis.

Author: Paul M. Gauthier
Publisher: Springer Science & Business Media
ISBN: 9401109346
Category : Mathematics
Languages : en
Pages : 565

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Proceedings of the NATO Advanced Study Institute and Séminaire de mathématiques supérieures, Montréal, Canada, July 26--August 6, 1993

Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 156

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Author: Rolf Nevanlinna
Publisher: Springer
ISBN: 3642855903
Category : Mathematics
Languages : en
Pages : 383

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Book Description
The present monograph on analytic functions coincides to a lar[extent with the presentation of the modern theory of single-value analytic functions given in my earlier works "Le theoreme de Picarc Borel et la theorie des fonctions meromorphes" (Paris: Gauthier-Villar 1929) and "Eindeutige analytische Funktionen" (Die Grundlehren dt mathematischen Wissenschaften in Einzeldarstellungen, VoL 46, 1: edition Berlin: Springer 1936, 2nd edition Berlin-Gottingen-Heidelberg Springer 1953). In these presentations I have strived to make the individual result and their proofs readily understandable and to treat them in the ligh of certain guiding principles in a unified way. A decisive step in thi direction within the theory of entire and meromorphic functions consiste- in replacing the classical representation of these functions through ca nonical products with more general tools from the potential theor (Green's formula and especially the Poisson-Jensen formula). On thi foundation it was possible to introduce the quantities (the characteristic the proximity and the counting functions) which are definitive for th

Author: William Blauvelet Woolf
Publisher:
ISBN:
Category : Functions, Meromorphic
Languages : en
Pages : 40

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Author: O.E. Lehto
Publisher: Springer
ISBN: 354037907X
Category : Mathematics
Languages : en
Pages : 408

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Author: Akademii︠a︡ nauk SSSR.
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 418

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Consists of abstracts in English.

Author: Kiyoshi Noshiro
Publisher: Springer Science & Business Media
ISBN: 3642859283
Category : Mathematics
Languages : en
Pages : 142

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Book 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.

Author: London Mathematical Society
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 1062

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