On a gap Tauberian theorem of Lorentz and Zeller
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- by T. A. Keagy PDF
- Proc. Amer. Math. Soc. 86 (1982), 459-460 Request permission
Abstract:
G. G. Lorentz and K. L. Zeller have stated an $O$-Tauberian theorem which places a restriction on the rate of absolute convergence of the row sums of a regular summability method. In this note, we prove a theorem that has as a corollary an extension of the above result in which this restriction is deleted.References
- David F. Dawson, A Tauberian theorem for stretchings, J. London Math. Soc. (2) 13 (1976), no. 1, 27–33. MR 404918, DOI 10.1112/jlms/s2-13.1.27
- David F. Dawson, Summability of matrix transforms of stretchings and subsequences, Pacific J. Math. 77 (1978), no. 1, 75–81. MR 510463
- J. A. Fridy, Tauberian theorems via block dominated matrices, Pacific J. Math. 81 (1979), no. 1, 81–91. MR 543735
- G. G. Lorentz and K. L. Zeller, $o$-but not $O$-Tauberian theorems, Proc. Amer. Math. Soc. 45 (1974), 401–404. MR 346370, DOI 10.1090/S0002-9939-1974-0346370-9
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 459-460
- MSC: Primary 40E15; Secondary 40C05
- DOI: https://doi.org/10.1090/S0002-9939-1982-0671215-1
- MathSciNet review: 671215