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On a Tauberian Theorem of G. Ricci1

Published online by Cambridge University Press:  20 January 2009

C. T. Rajagopal
C. T. Rajagopal
Affiliation:
Madras Christian College, Tambaram, S. India.
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I prove in this note some theorems on Rieszian and Dirichlet summabilities involving a Tauberian hypothesis with gaps. One of the theorems (§ 2, Theorem A) has been proved by Ricci [4, § 6] in a slightly less general form. Another theorem (§ 3) contains a Riesz version of a (C, k)-summability problem studied by Meyer-König [1, Satz 1].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 8 , Issue 3 , December 1949 , pp. 143 - 146
Copyright
Copyright © Edinburgh Mathematical Society 1949

References

REFERENCES

1.Meyer-König, Werner, “Limitierungsumkehrsätze mit Lückenbedingungen I,” Math. Zeitschrift, 45 (1939), 447–478.Google Scholar
2.Rajagopal, C. T. “On the limits of oscillation of a function and its Cesàro means,” Proc. Edinburgh Math. Soc. (2), 7 (1946), 162–167.Google Scholar
3.Rajagopal, C. T., “On Riesz summability and summability by Dirichlet's series,” American J. of Math., 59 (1947), 371–378.Google Scholar
4.Ricci, G., “Sui teoremi Tauberiani,” Annali di Matematica (IV), 13 (1935), 287–308.Google Scholar
5.Szász, O., “Über einige Saẗze von Hardy and Littlewood,” Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen (Mathematisch-Physikalische Klasse, 1930) 315–333.Google Scholar