Borel's Methods of Summability: Theory and Applications

di Bruce L. R. Shawyer (Autore)

Bruce Watson (Autore)

Oxford University Press, 1994

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.

• Autore: Bruce L. R. Shawyer, Bruce Watson
• Editore: Oxford University Press
• Collana: Oxford Mathematical Monographs
• Anno: 1994
• Rilegatura: Hardback
• Pagine: 254 p.
• Dimensioni: 241 x 162 mm
• Peso: 556 gr.
• EAN: 9780198535850

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