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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.
Produkteigenschaften
- Artikelnummer: 9780198535850
- Medium: Buch
- ISBN: 978-0-19-853585-0
- Verlag: OUP Oxford
- Erscheinungstermin: 14.07.1994
- Sprache(n): Englisch
- Auflage: Erscheinungsjahr 1994
- Produktform: Gebunden, HC gerader Rücken kaschiert
- Gewicht: 552 g
- Seiten: 254
- Format (B x H x T): 161 x 240 x 18 mm
- Ausgabetyp: Kein, Unbekannt