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A Note on the Absolute Nörlund Summability of Conjugate Fourier Series

Published online by Cambridge University Press:  09 April 2009

G. D. Dikshit
G. D. Dikshit
Affiliation:
University of Biafra, NsukkaUniversity of Auckland, Auckland, New Zealand
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Let σan be an infinite series, with sequence of partial sums {un}. Let {pn} be a sequence of constants, real or complex, and write Pn = po+p1+ … +pn The sequence-to-sequence transformation defines the sequence {tn} of Nörlund means of the sequence {u}, generated by the sequence {pn}. The series σan is said to be surnmable (N, pn), to sum s, if limn→∞ tn = s. It is said to be absolutely sum.mable (N, pn), or summable |N, pn|, if {tn} ∈BV.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 12 , Issue 1 , February 1971 , pp. 86 - 90
Copyright
Copyright © Australian Mathematical Society 1971

References

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