Characterization of summability points of Nörlund methods

Grosse-Erdmann, Karl-Goswin; Stadtmüller, Karin

doi:10.1090/S0002-9947-1995-1260167-5

Characterization of summability points of Nörlund methods
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by Karl-Goswin Grosse-Erdmann and Karin Stadtmüller

Trans. Amer. Math. Soc. 347 (1995), 2563-2574

DOI: https://doi.org/10.1090/S0002-9947-1995-1260167-5

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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 $f$.

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