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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1260167-5
PII: S 0002-9947(1995)1260167-5
Keywords: Power series, matrix transforms, Nörlund methods, summability points
Article copyright: © Copyright 1995 American Mathematical Society