Borel's methods of summability : theory and applications
Author(s)
Bibliographic Information
Borel's methods of summability : theory and applications
（Oxford mathematical monographs）
Clarendon Press , Oxford University Press, 1994
Available at / 35 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
SHA||66||1200021323804
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc20:515/sh282070306988
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Note
Includes bibliographical references (p. 207-238) and index
Description and Table of Contents
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.
Table of Contents
- 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
by "Nielsen BookData"
