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The Hausdorff Means for Double Sequences

Published online by Cambridge University Press:  20 November 2018

F. Ustina
F. Ustina*
Affiliation:
University of Alberta, Edmonton
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The basic theory of the Hausdorff means for double sequences was developed some thirty - three years ago by C.R. Adams [1], and independently by F. Hallenbach [3], Yet today, many of the properties of these means remain largely uninvestigated. The calculations here, although clearly more complex, for the most part break down into obvious modifications of the calculations in the one dimensional case.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 3 , August 1967 , pp. 347 - 352
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Adams, C. R., Hausdorff transformations for double sequences. Bull. Amer. Math. Soc. 39 (1933), 303-312.Google Scholar
2. Copping, J., Transformations of multiple sequences. Proc. London Math. Soc. (3) 6 (1955), 224-250.Google Scholar
3. Hallenbach, F., Zur Thèorie der Limitierungsverfahren von Doppelfolgen. Inaugural - Dissertation, Rheinischen Friedrich-Wilhelms - Universitát, Bonn (1933).Google Scholar
4. Hamilton, H. J., Transformations of multiple sequences. Duke Math. Jour. 2 (1933), 29-60.Google Scholar
5. Hardy, G. H., Divergent Series. Oxford University Press (1955).Google Scholar
6. Robison, G., Divergent double sequences and series. Trans. Amer. Math. Soc, 28 (1922), 50-73.Google Scholar
7. Ustina, F., Gibbs phenomenon and Lebesgue constants for theHausdorff means of double series. Ph. D. Dissertation, Alberta (1966).Google Scholar
8. Widder, D. V., The Laplace Transform. Princeton University Press (1944).Google Scholar