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Transactions of the American Mathematical Society

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Characterization of summability points of Nörlund methods


Authors: Karl-Goswin Grosse-Erdmann and Karin Stadtmüller
Journal: Trans. Amer. Math. Soc. 347 (1995), 2563-2574
MSC: Primary 30B10; Secondary 40D09, 40G05
DOI: https://doi.org/10.1090/S0002-9947-1995-1260167-5
MathSciNet review: 1260167
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Abstract: By a theorem of F. Leja any regular Nörlund method $ (N,p)$ sums a given power series $ f$ at most at countably many points outside its disc of convergence. This result was recently extended to a class of non-regular Nörlund methods by K. Stadtmüller. In this paper we obtain a more detailed picture showing how possible points of summability and the value of summation depend on $ p$ and $ f$.


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

  • [1] R. P. Agnew, Summability of power series, Amer. Math. Monthly 53 (1946), 251-259. MR 0015525 (7:433b)
  • [2] D. Borwein and A. Jakimovski, Matrix transformations of power series, Proc. Amer. Math. Soc. 122 (1994), 511-523. MR 1198451 (95a:47023)
  • [3] G. Bouligand, Sur la comparaison de certains procédés de sommation des séries divergentes, Enseign. Math. 26 (1927), 15-27.
  • [4] G. H. Hardy, Divergent series, Clarendon Press, Oxford, 1949. MR 0030620 (11:25a)
  • [5] F. Leja, Sur la sommation des séries entières par la méthode des moyennes, Bull. Sci. Math. 54 (1930), 239-245.
  • [6] K. Stadtmüller, Summability of power series by non-regular Nörlund-methods, J. Approx. Theory 68 (1992), 33-44. MR 1143959 (93e:40006)
  • [P] Vermes, The application of $ \gamma $-matrices to Taylor series, Proc. Edinburgh Math. Soc. (2) 8 (1948), 43-49. MR 0027349 (10:291g)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1260167-5
Keywords: Power series, matrix transforms, Nörlund methods, summability points
Article copyright: © Copyright 1995 American Mathematical Society

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