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Overview"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." Full Product DetailsAuthor: Bruce L. R. Shawyer (Professor of Mathematics, Professor of Mathematics, Memorial University of Newfoundland, Canada) , Bruce Watson (Professor of Mathematics, Professor of Mathematics, Memorial University of Newfoundland, Canada) , Bruce B. WatonPublisher: Oxford University Press Imprint: Clarendon Press Dimensions: Width: 16.20cm , Height: 1.90cm , Length: 24.10cm Weight: 0.556kg ISBN: 9780198535850ISBN 10: 0198535856 Pages: 254 Publication Date: 14 July 1994 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsIntroduction; 1. Historical Overview; 2. Summability Methods in General; 3. Borel's Methods of Summability; 4. Relations with the family of circle methods; 5. Generalisations; 6. Albelian Theorems; 7. Tauberian Theorems - I; 8. Tauberian Theorems - II; 9. Relationships with other methods; 10. Applications of Borel's Methods; ReferencesReviewsThe 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 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<br> Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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