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The absolute Euler summability of Fourier series

Published online by Cambridge University Press:  09 April 2009

B. Kwee
B. Kwee
Affiliation:
Department of Mathematics University of MalayaKuala LumpurMalaysia
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The series is said to be summable |Eα| (0 < α < 1) if where Sv = a0 + a1 … + av, and . Since (see [2]), (1) is equivalent to .

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 2 , March 1972 , pp. 129 - 140
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Bosanquet, L. S. and Kestleman, H., ‘The absolute convergence of a series of integrals’, Proc. London Math. Soc. (2), 45 (1939) 88–97.CrossRefGoogle Scholar
[2]Knopp, K. and Lorentz, G. G., ‘Beiträge zur absoluten Limitierung’, Arch. Math. 2 (1949–1950), 10–16.CrossRefGoogle Scholar
[3]Tripathy, N., ‘On the absolute Hausdorff summability of Fourier series’, Jour. London Math. Soc. 44 (1969), 15–25.CrossRefGoogle Scholar
[4]Whittaker, J. M., ‘The absolute summability of Fourier series’, Proc. Edinburgh Math. Soc. 2 (1930), 1–5.CrossRefGoogle Scholar