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On the Absolute Nörlund Summability of a Fourier Series

Published online by Cambridge University Press:  20 November 2018

D. S. Goel  and
B. N. Sahney
D. S. Goel
Affiliation:
University of Calgary, Calgary, Alberta
B. N. Sahney
Affiliation:
University of Calgary, Calgary, Alberta
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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)

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 4 , December 1973 , pp. 599 - 602
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Alexits, G., Convergence problems of orthogonal series, Pergamon Press, New York, 1961.Google Scholar
2. Bhatt, S. N., An aspect of the local property of |N, pn| summability of a Fourier series, Indian J. Math. 5 (1963), 87–91.Google Scholar
3. Hsiang, F. C., On the absolute Nörlund summability of a Fourier series, J. Austral. Math. Soc. 7 (1967), 252–256.Google Scholar