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Absolute Nörlund matrix summability of Fourier series based on inclusion theorems

Published online by Cambridge University Press:  24 October 2008

B. Kuttner  and
B. E. Rhoades
B. Kuttner
Affiliation:
Department of Pure Mathematics, University of Birmingham, Birmingham, B 15 2TT
B. E. Rhoades
Affiliation:
Department of Mathematics, Indiana University, Bloomington, Indiana 47405, U.S.A.
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Extract

In a recent paper [39] the second author established sufficient conditions for a Nörlund matrix (N, p) to be stronger than a Cesaro matrix (C, α) of order α, for some positive α. This result was then used to show that a number of known theorems dealing with the Nörlund summability of Fourier series, or related series, can be more easily established, since the conditions placed on the Nörlund matrix imply that it is stronger than some (C, α) method, for which the summability theorem has already been established.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 2 , March 1989 , pp. 319 - 333
Copyright
Copyright © Cambridge Philosophical Society 1989

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