ENGLISH

Borel's Methods of Summability: Theory and Application

By Bruce Watson , Bruce Shawyer

Book information

Publisher
Oxford University Press
Year
1994
ISBN
0198535856, 9780198535850
Language
english
Format
PDF
Filesize
4 MB (4369512 bytes)
Series
Oxford Mathematical Monographs
Pages
C, xii+242\255
DPI
600
Orientation
portrait
Paginated
yes
Scanned
yes
Time added
2014-03-16 07:33:06

Description

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. Readership: Research mathematicians.

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