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Some Theorems on Absolute Summability

Published online by Cambridge University Press:  20 November 2018

M. S. Macphail
M. S. Macphail*
Affiliation:
Carleton College, Ottawa
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A summation method defined by the linear transformation

will be called an l-l method if ∑|yr| < ∞ whenever ∑|xk| < ∞; if in addition we have ∑yr = ∑xk whenever ∑|xk| < ∞ we shall say the method is absolutely regular. (It should be observed that we are dealing with series-to-series methods, not sequence-to-sequence as usual.)

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951, pp. 386 - 390
Copyright
Copyright © Canadian Mathematical Society 1951

References

1. Agnew, R. P., Summability of power series, Amer. Math. Monthly, vol. 53 (1946), 251–259.Google Scholar
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3. Knopp, K. and Lorentz, G. G., Beiträge zur absoluten Limitierung, Archiv der Mathematik, vol. 2 (1949), 10–16.Google Scholar
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