Rate of Convergence for the Absolutely (C, α) Summable Fourier Series of Functions of Bounded Variation
✍ Scribed by Natalia Humphreys; Ranko Bojanic
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 97 KB
- Volume
- 101
- Category
- Article
- ISSN
- 0021-9045
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✦ Synopsis
A theorem of Bosanquet states that the Fourier series of a 2?-periodic function of bounded variation is absolutely (C, :) summable. In this paper we give a quantitative version of Bosanquet's result.
📜 SIMILAR VOLUMES
In this paper we study the rate of convergence of two Bernstein Be zier type operators B (:) n and L (:) n for bounded variation functions. By means of construction of suitable functions and the method of Bojanic and Vuillemier (J. Approx. Theory 31 (1981), 67 79), using some results of probability
Complementary spaces for Fourier series were introduced by G. Goes and generalized by M. Tynnov. In this paper we investigate a notion of complementary space for double Fourier series of functions of bounded variation. Various applications are given.
of Denton (Texas) (Eingegangen am 4.6. 1971) ## 1. Definitions Let a, be a giveninfinite series and let A, = il (n) be a positive inonotonic function of n tending t o infinity with n. We write The series z c n , i s said to he summable (R, An, r ) , r 2 0, t o sum s, if A > ( w ) / w ' --+ s, as