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Lebesgue Constants for Regular Taylor Summabllity

Published online by Cambridge University Press:  20 November 2018

R. L. Forbes
R. L. Forbes*
Affiliation:
University of Alberta, Calgary
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The nth Taylor mean of order r of a sequence {sn} is given by

1.1

where

1.2

Cowling [l] has shown that this method is regular if and only if 0 ≦ r < 1. Since r = 0 corresponds to ordinary convergence, it will be assumed here that 0 < r < 1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 6 , December 1965 , pp. 797 - 808
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Cowling, V. F., Summability and analytic continuation, Proc Amer. Math. Soc., Vol.1 (1950), pp. 536-542.Google Scholar
2. Ishiguro, K., The Lebesgue constants for (γ, r) summation of Fourier series, Proc. Japan Acad., Vol. 36, 1960, pp.470 Google Scholar
3. Livingston, A. E., The Lebesgue constants for (E, p) summation of Fourier series, Duke Math. Journ., Vol.21 (1954), pp. 309-314.Google Scholar
4. Lorch, L., The Lebesgue constants for Borel summability, Duke Math. Journ., Vol. 11, No.3 (Sept. 1944), pp. 459-467.Google Scholar
5. Lorch, L., The Lebesgue constants for (E, 1) summation of Fourier series, Duke Math. Journ., Vol.19 (1952), pp. 459-467.Google Scholar
6. Lorch, L. and Newman, D.J., The Lebesgue constants for (γ, r) summation of Fourier series, Can. Math. Bull., Vol. 6, No.2 (May 1963), pp. 179-182.Google Scholar
7. Miracle, C. L., The Gibbs phenomenon for Taylor means and for [F, dn] means, Can. Journ. Math., Vol.12(1960), pp. 660-673.Google Scholar