Borel's methods of summability : theory and applications

Bruce Shawyer and 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. 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.

「Nielsen BookData」より


  • Introduction
  • 1. Historical Overview
  • 2. Summability Methods in General
  • 3. Borel's Methods of Summability
  • 4. Relations with the family of circle methods
  • 5. Generalisations
  • 6. Albelian Theorems
  • 7. Tauberian Theorems - I
  • 8. Tauberian Theorems - II
  • 9. Relationships with other methods
  • 10. Applications of Borel's Methods
  • References

「Nielsen BookData」より


書名 Borel's methods of summability : theory and applications
著作者等 Shawyer, Bruce
Watson, Bruce
Waton Bruce B.
Watson Bruce B.
Shawyer Bruce L.R.
シリーズ名 Oxford mathematical monographs
出版元 Clarendon Press;Oxford University Press
刊行年月 1994
ページ数 xii, 242 p.
大きさ 25 cm
ISBN 9780198535850
NCID BA23205709
※クリックでCiNii Booksを表示
言語 英語
出版国 イギリス