On the Absolute Nörlund Summability of the Conjugate Series of a Fourier Series

1963 ◽  
Vol s1-38 (1) ◽  
pp. 204-214 ◽  
Author(s):  
T. Pati
Keyword(s):  
Fourier Series ◽  
Conjugate Series ◽  
The Absolute ◽  
Absolute Nörlund Summability

scholarly journals On the absolute Nörlund summability factors of a Fourier series and its conjugate series at a point

1978 ◽  
Vol 19 (2) ◽  
pp. 161-181
Author(s):  
Kôsi Kanno
Keyword(s):  
Fourier Series ◽  
Summability Factors ◽  
Conjugate Series ◽  
The Absolute ◽  
Absolute Nörlund Summability

The object of this paper is to give generalizations of Okuyama's Theorem [Bull. Austral. Math. Soc.12 (1975), 9–21, Tôohoku Math. J. (2) 28 (1976), 563–581] on the absolute Nörlund summability factors of a Fourier series and its conjugate series.Our theorems imply many results proved by other authors: especially Theorem 1 includes the results of Bhatt and Kishor [Indian J. Math.9 (1967), 259–267 (1968)], Dikshit [Pacific J. Math.63 (1976), 371–379], and Lal [Publ. Inst. Math. (Beograd) 20 (34) (1976), 169–178], and we can easily deduce Lal's result [Indian J. Math.16 (1974), 1–22] from our Corollary 2.

On the Absolute Nörlund Summability of a Fourier Series

1973 ◽  
Vol 16 (4) ◽  
pp. 599-602
Author(s):  
D. S. Goel ◽  
B. N. Sahney
Keyword(s):  
Fourier Series ◽  
Bounded Variation ◽  
Infinite Series ◽  
Partial Sums ◽  
The Absolute ◽  
Image Position ◽  
Absolute Nörlund Summability

Let be a given infinite series and {sn} the sequence of its partial sums. Let {pn} be a sequence of constants, real or complex, and let us write(1.1)If(1.2)as n→∞, we say that the series is summable by the Nörlund method (N,pn) to σ. The series is said to be absolutely summable (N,pn) or summable |N,pn| if σn is of bounded variation, i.e.,(1.3)

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