Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-20T13:27:00.594Z Has data issue: false hasContentIssue false
  • English
  • Français

Absolute total-effective (N, pn) means

Published online by Cambridge University Press:  24 October 2008

H. P. Dikshit
H. P. Dikshit
Affiliation:
University of Allahabad and University of Jabalpur, India
Get access Rights & Permissions [Opens in a new window]

Extract

1. Definitions and notations. Let be a given infinite series with the sequence of its partial sums {sn}. Let {pn} be a sequence of constants, real or complex, and let us write

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 1 , January 1971 , pp. 107 - 122
Copyright
Copyright © Cambridge Philosophical Society 1971

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)Astrachan, Max. Studies in the summabiity of Fourier series by Nörlund means. Duke Math. J. 2 (1936), 543–568.CrossRefGoogle Scholar
(2)Bosanquet, L. S.The absolute Cesàro summabiity of a Fourier series. Proc. London Math. Soc. 41 (1936), 517–528.CrossRefGoogle Scholar
(3)Bosanquet, L. S. and Hyslop, J. M.On the absolute summability of the allied series of a Fourier series. Math. Z. 42 (1937), 487–512.CrossRefGoogle Scholar
(4)Dikshit, H. P.On the summability |N, pn|, of a Fourier series at a point. Proc. Cambridge Philos. Soc. 65 (1969), 495–505.CrossRefGoogle Scholar
(5)Dikshit, H. P.Absolute summability of a Fourier series by Nörlund means, Math. Z. 102 (1967), 166–170.CrossRefGoogle Scholar
(6)Dikshit, H. P. Absolute summabiity of a Fourier series and its derived series by a product method (communicated).Google Scholar
(7)Hyslop, J. M.On the absolute summabiity of the successively derived series of Fourier series and its allied series. Proc. London Math. Soc. 46 (1940), 55–80.CrossRefGoogle Scholar
(8)Kuttner, B.Note on the ‘second theorem of coistency’ for Riesz summability. J. London Math. Soc. 26 (1951), 104–111.CrossRefGoogle Scholar
(9)Pati, T.On the absolute summability of Fourier series by Nörlund means. Math. Z. 88 (1965), 244–249.CrossRefGoogle Scholar
(10)Titchmarsh, E. C.The theory of functions (Oxford, 1957).Google Scholar