Buch, Englisch, 254 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 552 g
Theory and Application
Buch, Englisch, 254 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 552 g
Reihe: Oxford Mathematical Monographs
ISBN: 978-0-19-853585-0
Verlag: OUP Oxford
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.
