The theory of cluster sets
Author(s)
Bibliographic Information
The theory of cluster sets
(Cambridge tracts in mathematics and mathematical physics, no. 56)
Cambridge University Press, 2004
- : pbk
Available at 3 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
"First published 1966, first paperback edition 2004"--T.p. verso
Bibliography: p. 190-205
Includes indexes
Description and Table of Contents
Description
The book provides an introduction to the theory of cluster sets, a branch of topological analysis which has made great strides in recent years. The cluster set of a function at a particular point is the set of limit values of the function at that point which may be either a boundary point or (in the case of a non-analytic function) an interior point of the function's domain. In topological analysis, its main application is to problems arising in the theory of functions of a complex variable, with particular reference to boundary behaviour such as the theory of prime ends under conformal mapping. An important and novel feature of the book is the discussion of more general applications to non-analytic functions, including arbitrary functions. The authors assume a general familiarity with classical function theory but include the more specialised material required for the development of the theory of cluster sets, so making the treatment accessible to graduate students.
Table of Contents
- Preface
- 1. Introduction
- 2. Functions analytic in a circular disc
- 3. Topics in the theory of conformal mapping
- 4. Intrinsic properties of cluster sets
- 5. Cluster sets of functions analytic in the unit disc
- 6. Boundary theory in the large
- 7. Boundary theory in the small
- 8. Further boundary properties of functions meromorphic in the disc. classification of singularities
- 9. Prime ends
- Bibliography
- Index of symbols
- Index.
by "Nielsen BookData"