Borel's Methods of Summability: Theory and Applications

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Clarendon Press, 1994 - History - 242 pages
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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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About the author (1994)

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

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