Borel's methods of summability : theory and applications
著者
書誌事項
Borel's methods of summability : theory and applications
（Oxford mathematical monographs）
Clarendon Press , Oxford University Press, 1994
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注記
Includes bibliographical references (p. 207-238) and index
内容説明・目次
内容説明
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.
目次
- 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
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