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On the absolute Nörlund summability of a Fourier series

Published online by Cambridge University Press:  09 April 2009

Fu Cheng Hsiang
Fu Cheng Hsiang
Affiliation:
National Taiwan UniversityTaipei, Formosa, China
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Let Σn−0∞an, 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

If

as n → ∞, then we say that the series is summable by the Nörlund method (N, pn) to σ And the series a,Σan, is said to be absolutely summable (N, pn) or summable |N, Pn| if {σn} is of bounded variation, i.e.,

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 2 , May 1967 , pp. 252 - 256
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Bhatt, S. N., ‘An aspect of local property of |N, pn| summability of a Fourier series’, Indian Journ. Math., 5 (1963), 87–91.Google Scholar
[2]McFadden, L., ‘Absolute Nörlund summability’, Duke Math. Journ., 9 (1942), 168–207.CrossRefGoogle Scholar