scholarly journals On the absolute summability factor of Fourier series

1981 ◽  
Vol 24 (3) ◽  
pp. 327-337
Author(s):  
Yasuo Okuyama
Keyword(s):  
Fourier Series ◽  
General Theorem ◽  
Absolute Summability ◽  
Summability Factor ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
The Absolute ◽  
Tohoku Math

The purpose of this paper is to give a general theorem on the absolute Riesz summability factor of Fourier series which implies Matsumoto's Theorem [Tôhoku Math. J. 8 (1956), 114–124] and to deduce some results from the theorem.

scholarly journals On absolute generalized N"orlund summability of orthogonal series

2002 ◽  
Vol 33 (2) ◽  
pp. 161-166
Author(s):  
Y. Okuyama
Keyword(s):  
Orthogonal Series ◽  
General Theorem ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
The Absolute

In this paper, we shall prove a general theorem which contains two theorems on the absolute N"orlund summability and the absolute Riesz summability of orthogonal series.

scholarly journals On absolute riesz summability of Fourier series

1975 ◽  
Vol 19 (1) ◽  
pp. 97-102
Author(s):  
G. D. Dikshit
Keyword(s):  
Fourier Series ◽  
General Theorem ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
Summability Of Fourier Series ◽  
Image Position

AbstractLet and .In 1951 Mohanty proved the following theorem: .In this paper a general theorem on summability |R,l (w), 1 | of Σ An(x) has been given which improves upon Mohanty's result in different ways (see Corollaries 1, 2 and 3) and it is also shown that some of the results of this note are the best possible.

Absolute Riesz summability of a Fourier related series, II

1985 ◽  
Vol 32 (1) ◽  
pp. 93-102
Author(s):  
G.D. Dikshit
Keyword(s):  
Fourier Series ◽  
Periodic Function ◽  
General Theorem ◽  
Partial Sums ◽  
Suitable Constant ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
Related Series

This paper is an endeavour to improve upon the work begun in an earlier paper with the same title. We prove a general theorem on the summability |R, exp((log ω)β+1), ρ| of the series ∑ {sn(x)−s}/n, where {sn(x)} is the sequence of partial sums at a point x of the Fourier series of a Lebesgue integrable 2π-periodic function and s is a suitable constant. While the theorem improves upon the main result contained in the previous paper, corollaries to it include recent results due to Chandra and Yadava.

Sign in / Sign up

Export Citation Format

Share Document