Tauberian Theorems for Weighted Means of Double Sequences
โ Scribed by Chang-Pao Chen; Jui-Ming Hsu
- Book ID
- 110228278
- Publisher
- Springer
- Year
- 2000
- Tongue
- English
- Weight
- 265 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0133-3852
No coin nor oath required. For personal study only.
๐ 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.
Let (x jk : j, k = 0, 1, 2, . . .) be a double sequence of real or complex numbers, and set x jk for m, n = 0, 1, 2, . . . . We give necessary and sufficient conditions, under which st-lim ฯ mn = ฮพ implies st-lim x jk = ฮพ, where ฮพ is a finite number. These Tauberian conditions are one-sided when th