Borel's Methods of Summability: Theory and Applications by Bruce L. R. ShawyerBorel's Methods of Summability: Theory and Applications by Bruce L. R. Shawyer

Borel's Methods of Summability: Theory and Applications

byBruce L. R. Shawyer, Bruce Watson

Hardcover | March 1, 1995

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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.
Bruce L. R. Shawyer is at Memorial University of Newfoundland. Bruce Watson is at Memorial University of Newfoundland.
Title:Borel's Methods of Summability: Theory and ApplicationsFormat: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.