Description
Oxford University Press Borel'S Methods Of Summability : Theory And Applications by Bruce L. R. Shawyer , Bruce Watson
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.Borels 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.show more