Local property of absolute Riesz summability of fourier series

1984 ◽  
pp. 77-90
Author(s):  
Yasuo Okuyama
Keyword(s):  
Fourier Series ◽  
Local Property ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
Summability Of Fourier 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.

scholarly journals Absolute Riesz summability of Fourier series and their conjugate series

1970 ◽  
Vol 3 (2) ◽  
pp. 217-229
Author(s):  
Masako Izumi ◽  
Shin-ichi Izumi
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Functions Of Bounded Variation ◽  
Conjugate Series ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
Summability Of Fourier Series ◽  
Series Of Functions

This paper contains two theorems. The first theorem treats the |R, r, l| summability of Fourier series and their associated series of functions of bounded variation. The second concerns the |R, r, l| summability of Fourier series of functions f such that φ(t)m(l/t) is of bounded variation where m(u) increases to infinity as u → ∞. These theorems generalize Mohanty's theorems.

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