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The Theory of Cluster Sets : Cambridge Tracts in Mathematics - E. F. Collingwood

The Theory of Cluster Sets

Cambridge Tracts in Mathematics

Paperback

Published: 2nd August 2004
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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.

Preface
Introduction
Functions analytic in a circular disc
Topics in the theory of conformal mapping
Intrinsic properties of cluster sets
Cluster sets of functions analytic in the unit disc
Boundary theory in the large
Boundary theory in the small
Further boundary properties of functions meromorphic in the disc. classification of singularities
Prime ends
Bibliography
Index of symbols
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521604819
ISBN-10: 0521604818
Series: Cambridge Tracts in Mathematics
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 224
Published: 2nd August 2004
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 21.6 x 14.0  x 1.3
Weight (kg): 0.29