Borel's Methods of Summability

Theory and Application
Erscheinungsjahr 1994
ISBN: 978-0-19-853585-0
Verlag: OUP Oxford

Buch, Englisch, 254 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 552 g

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.

Autoren/Hrsg.

Shawyer, Bruce L. R.

Watson, Bruce

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

Inhaltsverzeichnis

- 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