Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T15:17:01.664Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Tauberian theorem for absolute harmonic summability

Published online by Cambridge University Press:  24 October 2008

O. P. Varshney  and
Govind Prasad
O. P. Varshney
Affiliation:
Department of Mathematics, University, Roorkee, India
Govind Prasad
Affiliation:
Department of Mathematics, University, Roorkee, India
Get access Rights & Permissions [Opens in a new window]

Extract

Let Σan be a given infinite series with the sequence of partial sums {Sn}. Let the sequence be defined by

where is given by

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 1 , January 1969 , pp. 93 - 99
Copyright
Copyright © Cambridge Philosophical Society 1969

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hardy, G. H. and Littlewood, J. E.New convergence criteria for Fourier series. J. London Math. Soc. 7 (1932), 252–256.Google Scholar
(2)Iyengar, K. S. K.A Tauberian theorem and its application to convergence of Fourier series. Proc. Indian Acad. Sci. Sect. A 18 (1943), 81–87.Google Scholar
(3)Mohanty, R.A criterion for the absolute convergence of a Fourier series. Proc. London Math. Soc. 51 (1949), 186–196.Google Scholar
(4)Rajagopal, C. T.On the Nörlund summability of Fourier series. Proc. Cambridge Philos. Soc. 59 (1963), 47–53.Google Scholar
(5)Rangachari, M. S.Remarks on some Tauberian theorems for Nörlund summability. Indian J. Math. 3 (1961), 73–76.Google Scholar
(6)Varshney, O. P.On the absolute summability of Fourier series by a Nörlund method. University Roorkee Research Journ. 6 (1963), 103–113.Google Scholar