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Some Tauberian Theorems for the Logarithmic Method of Summability

Published online by Cambridge University Press:  20 November 2018

B. Kwee
B. Kwee*
Affiliation:
University of Malay ay Kuala Lumpur, Malaysia
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The series is said to be summable (L) to s if the sequence {sn}, where sn = a0 + a1 + … + an, is L-convergent to s, i.e., if

If the sequence {sn} is l-convergent to s, i.e., if the sequence {tn}, where

1

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1324 - 1331
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Agnew, R. P., Abel transforms and partial sums of Tauberian series, Ann. of Math. (2) 50 (1949), 110–117.Google Scholar
2. Borwein, D., A logarithmic method of summability, J. London Math. Soc. 83 (1958), 212–220.Google Scholar
3. Hardy, G. H., Divergent series (Oxford, at the Clarendon Press, 1949).Google Scholar
4. Hsiang, F. C., Summability (L) of the Fourier series, Bull. Amer. Math. Soc. 67 (1961), 150–153.Google Scholar
5. Ishiguro, K., A converse theorem on the summability methods, Proc. Japan Acad. 39 (1963), 38–41.Google Scholar
6. Kwee, B., A Tauberian theorem for the logarithmic method of summation, Proc. Cambridge Philos. Soc. (to appear).Google Scholar
7. Mohanty, R. and Nanda, M., The summability (L) of the differentiated Fourier series, Quart. J. Math. Oxford Ser. 13 (1962), 40–44.Google Scholar
8. Nanda, M., The summability (L) of the Fourier series and the first differentiated Fourier series, Quart. J. Math. Oxford Ser. 13 (1962), 229–234.Google Scholar