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On (J, pn)-summability of Fourier series

Published online by Cambridge University Press:  20 January 2009

F. M. Khan
F. M. Khan
Affiliation:
Department of Mathematics and Statistics, Aligarh Muslim University, Aligarh, India
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Let pn>0 be such that pn diverges, and the radius of convergence of the power series

is 1. Given any series σan with partial sums sn, we shall use the notation

and

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 1 , June 1972 , pp. 13 - 17
Copyright
Copyright © Edinburgh Mathematical Society 1972

References

REFERENCES

(1) Borwein, D., On methods of summability based on power series, Proc. Roy. Soc. Edinburgh 64 (1957), 342–348.Google Scholar
(2) Hardy, G. H., Divergent Series (Oxford, 1949).Google Scholar
(3) Hsiang, F. C., Summability (L) of the Fourier series, Bull. Amer. Math. Soc. 67 (1961), 150–153.CrossRefGoogle Scholar
(4) Titchmarsh, E. C., The Theory of Functions (Oxford, 1939).Google Scholar