Borel's Methods of Summability - Bruce L. R. Shawyer, Bruce Watson

Borel's Methods of Summability

Theory and Applications
Buch | Hardcover
254 Seiten
1994
Clarendon Press (Verlag)
978-0-19-853585-0 (ISBN)
104,75 inkl. MwSt
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.

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

Erscheint lt. Verlag 14.7.1994
Reihe/Serie Oxford Mathematical Monographs
Verlagsort Oxford
Sprache englisch
Maße 162 x 241 mm
Gewicht 556 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
ISBN-10 0-19-853585-6 / 0198535856
ISBN-13 978-0-19-853585-0 / 9780198535850
Zustand Neuware
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