Tauberian Theorems for Sequences linked by a Convolution
β Scribed by Richard Warlimont
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 669 KB
- Volume
- 193
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
β¦ Synopsis
Given sequences 9 , X : IN0 + C , g(0) = 1, linked by the convolution X * g = 9' (g'(n) := (n + 1)g(n + 1)) we study what can be inferred about X (n --f m) from some concrete information about the behaviour of g (n + 00).
π SIMILAR VOLUMES
We discuss the relations between power series methods, weighted mean methods, and ordinary convergence for double sequences. In particular, we study Tauberian theorems for methods being products of the related one-dimensional summability methods.
We study the asymptotic behavior of a family of sequences defined by the following nonlinear induction relation c 0 = 1 and c n = k j=1 r j c n/m j + k j=k+1 r j c n+1 1/m j -1 for n β₯ 1, where the r j are real positive numbers and m j are integers greater than or equal to 2. Depending on the fact t