A structure theorem for the absolute Riesz summability of the conjugate series of a fourier series

1968 ◽  
Vol 17 (1) ◽  
pp. 19-30
Author(s):  
B. D. Malviya
Keyword(s):  
Fourier Series ◽  
Structure Theorem ◽  
Conjugate Series ◽  
Riesz Summability ◽  
Absolute Riesz Summability ◽  
The Absolute

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 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.

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.

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