scholarly journals Absolute Riesz summability factors of Fourier series

1984 ◽  
Vol 36 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Kôsi Kanno
Keyword(s):  
Fourier Series ◽  
Summability Factors ◽  
Riesz Summability ◽  
Absolute Riesz Summability

scholarly journals Absolute Riesz summability factors for Fourier series

1970 ◽  
Vol 17 (1) ◽  
pp. 65-70
Author(s):  
Prem Chandra
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Summability Factors ◽  
Monotonic Sequence ◽  
Riesz Mean ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
Image Position

Let ∑an be a given infinite series and {λn} a non-negative, strictly increasing, monotonic sequence, tending to infinity with n. We write, for w > λ0,and, for r>0, we write is known as the Riesz sum of “ type ” λn and “ order ” r, andis called the Riesz mean of type λn and order r.

On absolute Riesz summability factors of infinite series and their application to Fourier series

2019 ◽  
Vol 26 (3) ◽  
pp. 361-366
Author(s):  
Hüseyin Bor
Keyword(s):  
Fourier Series ◽  
Infinite Series ◽  
Summability Method ◽  
Trigonometric Fourier Series ◽  
Summability Factors ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
The Absolute

Abstract In this paper, some known results on the absolute Riesz summability factors of infinite series and trigonometric Fourier series have been generalized for the {\lvert\bar{N},p_{n};\theta_{n}\rvert_{k}} summability method. Some new and known results are also obtained.

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.

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