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Tauberian Estimates Concerning the Regular Hausdorff and [J, f(x)] Transformations

Published online by Cambridge University Press:  20 November 2018

A. Meir
A. Meir*
Affiliation:
The University of Alberta, Calgary
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Denote by {t(x)} some linear transform of the sequence

of the form

where x attains continuous or only integer values. The problem of estimating |t(x) — sm| as x and m tend to ∞ with some connection between them was considered first by H.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 288 - 301
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Agnew, R. P., Abel transforms and partial sums of Tauberian series, Ann. Math., 50 (1949), 110–17.Google Scholar
2. Garten, V., Uber Taubersche Konstanten bel Cesàroschen Mittelbildungen, Comm. Math. Helv., 25 (1951), 311–35.Google Scholar
3. Hadwiger, H., Über ein Distanztheorem bei der A-Limitierung, Comm. Math. Helv., 16 (1944), 209–14.Google Scholar
4. Hartman, P., Taubers theorem and absolute constants, Amer. J. Math., 69 (1947), 599–606.Google Scholar
5. Jakimovski, A., Tauberian constants for Hausdorff transformations, Bull. Res. Council Isr., 94 (1961), 175-84.Google Scholar
6. Jakimovski, A., Tauberian constants for the [J,f(x)] transformations, Pac. J. Math., 12 (1962), 567–76.Google Scholar
7. Jakimovski, A., Sequence-to-function analogues to Hausdorff-transformations. Bull. Res. Council Isr., 8F (1960), 135–54.Google Scholar