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.
| ISBN: | 9780198535850 |
| Publication date: | 14th July 1994 |
| Author: | Bruce L R Professor of Mathematics, Professor of Mathematics, Memorial University of Newfoundland, Canada Shawyer, Watson |
| Publisher: | Clarendon Press an imprint of Oxford University Press |
| Format: | Hardback |
| Pagination: | 254 pages |
| Series: | Oxford Mathematical Monographs |
| Genres: |
Calculus and mathematical analysis Number theory |