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A Criterion for Taylor Summability of Fourier Series

Published online by Cambridge University Press:  20 November 2018

A. S. B. Holland ,
B. N. Sahney  and
J. Tzimbalario
A. S. B. Holland
Affiliation:
Department of Mathematics, University of Calgary, Calgary, Alberta T2N 1N4
B. N. Sahney
Affiliation:
Department of Mathematics, University of Calgary, Calgary, Alberta T2N 1N4
J. Tzimbalario
Affiliation:
Summer Research Institute, 1975, Department of Mathematics, University of Calgary, Calgary Alberta T2N 1N4
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Let {ank} be a matrix defined by

1

and n taking only non-negative integer values.

Let f(x) ∈ L [0, 2π] and be periodic with period 2π outside this interval. Let the Fourier series associated with the function f(x) be given by

and let

where s is a constant.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 3 , 01 September 1979 , pp. 345 - 350
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Forbes, R. L., Lebesgue constants for regular Taylor summability, Canad. Math. Bull. 8 (1965), p. 797-808.Google Scholar
2. Hardy, G. L., Divergent series (Oxford University Press 1956).Google Scholar
3. Holland, A. S. B., Sahney, B. N., and Tzimbalario, J., A criterion for Euler summability of Fourier series Bull. U.M.I. 12 (1975) p. 315-320.Google Scholar
4. Ishiguro, K., The Lebesgue constants for (γ, r) summation of Fourier series, Proc. Japan Acad. 36 (1960), p. 470-476.Google Scholar
5. Lorch, L. and Newman, D. J., The Lebesgue constants for (γ, r) summation of Fourier series, Canad. Math. Bull. 6 (1963), p. 179-182.Google Scholar
6. Miracle, C. L., The Gibbs phenomenon for Taylor mean and for [F, dn] means, Canad. Journ. Math. 12 (1960), p. 660-673.Google Scholar
7. Shaney, B. N. and Kathal, P. D., A new criterion for Borel summability of Fourier series, Canad. Math. Bull. 12 (1969), 573-579.Google Scholar
8. Zygmund, A., Trigonometric series, Cambridge University Press, (1960).Google Scholar