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On strong Rieszian summability

Published online by Cambridge University Press:  18 May 2009

Martin Glatfeld
Martin Glatfeld
Affiliation:
Mathematisches Institut Deb Universität, Göttingen
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Recently H.-E. Richert [10] introduced a new method of summability, for which he completely solved the “summability problem” for Dirichlet series, and which led also to an extension of our knowledge of the relations between the abscissae of ordinary and absolute Rieszian summability. This non-linear method, which may best be characterized by the notion “strong Rieszian summability” †, depends on three parameters, on the order k;, the type λ, and the index p;. While Richert's paper deals almost exclusively with the application of that method of summability in a specialized form (namely the case p = 2, λn=log n) to Dirichlet series, it is the object of the present paper, to consider the general theory of strong Rieszian summability.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 3 , December 1957 , pp. 123 - 131
Copyright
Copyright © Glasgow Mathematical Journal Trust 1957

References

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