BOREL'S METHODS OF SUMMABILITY by Bruce L. R. Shawyer, Bruce Watson ( 9780198535850 )

Item Details

Title:

BOREL'S METHODS OF SUMMABILITY
THEORY AND APPLICATIONS

By:

Bruce L. R. Shawyer, Bruce Watson

Format:

Hardback

List price:

£89.00

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£77.88

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ISBN 10:

0198535856

ISBN 13:

9780198535850

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Publisher:

OXFORD UNIVERSITY PRESS

Pub. date:

14 July, 1994

Series:

Oxford Mathematical Monographs

Pages:

254

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.

Synopsis:

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.

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Imprint:

Clarendon Press

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Returnable

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