Article contents
On Banach Limit of Fourier Series and Conjugate Series I
Published online by Cambridge University Press: 20 November 2018
Extract
Let (xn) be a sequence of real numbers. (xn) corresponds to a number Lim xn called the Banach limit of (xn) satisfying the following conditions:
(1) Lim (axn + byn) = a Lim xn + b Lim yn
(2) If xn ≥ 0 for every n, then Lim xn ≥ 0
(3) Lim xn+1 = Lim xn
(4) If xn = 1 for every n, then Lim xn = 1
The existence of such limits is proved by Banach [1].
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1968
References
- 2
- Cited by