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Product details:
- Publisher Clarendon Press
- Date of Publication 14 July 1994
- ISBN 9780198535850
- Binding Hardback
- No. of pages254 pages
- Size 241x162x19 mm
- Weight 556 g
- Language English 0
Categories
Short description:
BL The only new text to provide recent developments and applications in an expanding field Borel's methods of summability are fundamental to a whole class of sequences to function methods. With increasing application to problems of theoretical physics, these methods are enjoying a surge in research interest. This book covers both the theory and application of these methods, and will prove an invaluable reference for all number theorists.
MoreLong description:
Summability methods are transformations that map sequences (or functions) to sequences (or functions). A prime requirement for a "good" summability method is that it preserves convergence. Unless it is the identity transformation, it will do more: it will transform some divergent sequences to convergent sequences.
An important type of theorem is called a Tauberian theorem. Here, we know that a sequence is summable. The sequence satisfies a further property that implies convergence.
Borel's methods are fundamental to a whole class of sequences to function methods. The transformation gives a function that is usually analytic in a large part of the complex plane, leading to a method for analytic continuation.
These methods, dated from the beginning of the 20th century, have recently found applications in some problems in theoretical physics.
The treatment is careful and clear throughout. The Book will be a valuable work of reference in its field for many years to come. Mathematical Reviews
Table of Contents:
Introduction
Historical Overview
Summability Methods in General
Borel's Methods of Summability
Relations with the family of circle methods
Generalisations
Albelian Theorems
Tauberian Theorems - I
Tauberian Theorems - II
Relationships with other methods
Applications of Borel's Methods
References
