Borels Methods of Summability: Theory and Applications

Hardcover | March 1, 1995

byBruce L. R. Shawyer, Bruce Watson

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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 sequencesto 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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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 sequencesto convergent sequences. An important type o...

Bruce L. R. Shawyer is at Memorial University of Newfoundland. Bruce Watson is at Memorial University of Newfoundland.

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Format:HardcoverDimensions:254 pages, 9.21 × 6.14 × 0.75 inPublished:March 1, 1995Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198535856

ISBN - 13:9780198535850

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Table of Contents

Introduction1. Historical Overview2. Summability Methods in General3. Borel's Methods of Summability4. Relations with the family of circle methods5. Generalisations6. Albelian Theorems7. Tauberian Theorems - I8. Tauberian Theorems - II9. Relationships with other methods10. Applications of Borel's MethodsReferences

Editorial Reviews

`The book is written in a very informative style providing proofs where they support the understanding and referring to the literature for technical details and further study; the reader will very soon notice and appreciate the authors' thorough way of referencing.'W Beekmann, Zentrallblatt for Mathematik, Band 840/96.