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On Tauberian theorems for Abel-Cesàro summability

Published online by Cambridge University Press:  18 May 2009

C. T. Rajagopal
C. T. Rajagopal
Affiliation:
Ramanujan Institute of Mathematics, Madras, India
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For a series Σan with partial sums An=a0 + a1 + … + an(n ≥ 0), supposed to be real in this note, we define, in a generally accepted notation ([2], pp. 7, 9, 94–98), the following transforms:

(C, α) sequence-transform,

(H, k)sequence-transform (k = 0, 1, 2, …):

(A: C, α)fnunction-transform,

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 3 , Issue 4 , July 1958, pp. 176 - 181
Copyright
Copyright © Glasgow Mathematical Journal Trust 1958

References

REFERENCES

1.Amir, A. (Jakimovski), On a converse of Abel's theorem, Proc. Amer. Math. Soc., 3 (1952), 244–256.CrossRefGoogle Scholar
2.Hardy, G. H., Divergent series (Oxford, 1949).Google Scholar
3.Hausdorff, F., Die Äquivalenz der Hölderschen und Cesàroschen Grenzwerte negativer Ordnung, Math. Z., 31 (1930), 180–196.CrossRefGoogle Scholar
4.Karamata, J., Neuer Beweis und Verallgemeinerung der Tauberschen Sätze, welche die Laplacesche und Stieltjessehe Transformation betreffen, J. Reine Angew. Math., 164 (1931), 27–39.CrossRefGoogle Scholar
5.Knopp, K., On the proof of the main Tauberian theorem for the Ck- and Hk-methods, Proc. Amer. Math. Soc., 5 (1954), 571–573.Google Scholar
6.Kogbetliantz, E., Sommation des séries et intégrales divergences par les moyennes arithémitiguea et typiques, Mémor Sci. Math. LI (Paris, 1931).Google Scholar
7.Lord, R. D., On some relations between the Abel, Borel and Cesàro methods of summation, Proc. London Math. Soc. (2), 38 (1935), 241–256.CrossRefGoogle Scholar
8.Parameswaran, M. R. and Jakimovski, A., Generalized Tauberian theorems for summability (A), Quart. J. Math. Oxford (2). To appear shortly.Google Scholar
9.Rajagopal, C. T. and Jakimovski, A., Applications of a theorem of O. Szász for the product of Cesaro and Laplace transforms, Proc. Amer. Math. Soc., 5 (1954), 370–384.Google Scholar
10.Rajagopal, C. T., Theorems on the product of summability methods with applications, J. Indian Math. Soc.(N.S.), 18 (1954), 89–105.Google Scholar
11.Rajagopal, C. T., Simplified proofs of some Tauberian theorems of Jakimovski, Pacific J. Math., 7 (1957), 955–960, with addendum and corrigendum, Pacific J. Math.CrossRefGoogle Scholar
12.Szász, O., Collected mathematical papers (Cincinnati, 1955).Google Scholar