✦ LIBER ✦
Tauberian theorems for double sequences that are statistically summable (C,1,1)
✍ Scribed by Ferenc Móricz
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 187 KB
- Volume
- 286
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
✦ Synopsis
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 σ mn = ξ implies st-lim x jk = ξ, where ξ is a finite number. These Tauberian conditions are one-sided when the x jk are real numbers, and they are two-sided when the x jk are complex numbers. In particular, these Tauberian conditions are clearly satisfied if (x jk ) is statistically slowly decreasing in the case of real sequences or if (x jk ) is statistically slowly oscillating in the case of complex sequences.