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$ o$-but not $ O$-Tauberian theorems


Authors: G. G. Lorentz and K. L. Zeller
Journal: Proc. Amer. Math. Soc. 45 (1974), 401-404
MSC: Primary 40E05
DOI: https://doi.org/10.1090/S0002-9939-1974-0346370-9
MathSciNet review: 0346370
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Abstract: Let $ A$ be a regular matrix summability method. Relations between different Tauberian theorems for $ A$ are discussed. We show that most summability methods possess some $ o$-Tauberian theorem with the property that the corresponding $ O$-Tauberian theorem is not valid.


References [Enhancements On Off] (What's this?)

  • [1] G. G. Lorentz, Tauberian theorems and Tauberian conditions, Trans. Amer. Math. Soc. 63 (1948), 226-234. MR 9, 425. MR 0023932 (9:425d)
  • [2] -, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190. MR 10, 367. MR 0027868 (10:367e)
  • [3] M. Stieglitz, Die allgemeine Form der $ O$-Tauber-Bedingung für das EulerKnopp- und Borel-Verfahren, J. Reine Angew. Math. 246 (1971), 172-179. MR 42 #8132. MR 0273251 (42:8132)
  • [4] K. Zeller and W. Beekmann, Theorie der Limitierungsverfahren, 2nd ed., Ergebnisse der Math. und ihrer Grenzgebiete, Band 15, Springer-Verlag, Berlin and New York, 1970. MR 41 #8863. MR 0264267 (41:8863)

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DOI: https://doi.org/10.1090/S0002-9939-1974-0346370-9
Article copyright: © Copyright 1974 American Mathematical Society

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