Borel's Methods of Summability : Theory and Applications
Book Details
Format
Hardback or Cased Book
Book Series
Oxford Mathematical Monographs
ISBN-10
0198535856
ISBN-13
9780198535850
Publisher
Oxford University Press
Imprint
Clarendon Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jul 14th, 1994
Print length
254 Pages
Weight
556 grams
Dimensions
24.10 x 16.20 x 1.90 cms
Product Classification:
Number theoryCalculus & mathematical analysis
Ksh 18,300.00
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Summability methods are concerned with transforming series of numbers to other series. It is an area that has seen applications in number theory as well as in other parts of mathematics. This book covers both the theory and some of the applications of Borel summability.
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.
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