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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.)

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
4. Macphail, M. S., Euler'Knopp summability of classes of convergent series, Amer. J. Math., vol. 68 (1946), 449–450.Google Scholar
5. Mazur, S., Eine Anwendung der Théorie der Operationen bei der Untersuchung der Toeplitzschen Limitierungsverfahren, Studia Mathematica, vol. 2 (1930), 40–50.Google Scholar