Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T11:10:28.614Z Has data issue: false hasContentIssue false
  • English
  • Français

On the absolute summability of some series related to a Fourier series

Published online by Cambridge University Press:  24 October 2008

B. K. Ray
B. K. Ray
Affiliation:
Parida Building, Kanika Road, Cuttack-1, Orissa, India
Get access Rights & Permissions [Opens in a new window]

Extract

1.Introduction. 1.1. Let f(t) be a periodic function with period 2π and integrable in the Lebesgue sense over ( -π,π). We assume as we may without loss of generality, that the Fourier series of f(t) is .

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 1 , January 1970 , pp. 29 - 45
Copyright
Copyright © Cambridge Philosophical Society 1970

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)Bosanquet, L. S. and Kestelman, H.The absolute convergence of series of integrals. Proc. London Math. Soc. (2), 45 (1939), 88–97.Google Scholar
(2)Haslam-Jones, U. S.A note on the Fourier coefficients of unbounded functions. J. London Math. Soc. 2 (1927), 151–154.Google Scholar
(3)Matsumoto, K.On the absolute Cesàro summability of a series related to a Fourier Series. Tôhoku Math. J.. 8 (1956), 205–222.Google Scholar
(4)Mazhar, S. M.A Tauberian theorem for absolute summability. Indian J. Math. 1 (1959), 69–76.Google Scholar
(5)Mohanty, R.On the absolute Riesz summability of Fourier series and allied series. Proc. London Math. Soc. (2), 52 (1951), 295–320.Google Scholar
(6)Mohanty, R.On the convergence factor of a Fourier series. Proc. Cambridge Philos. Soc. 63 (1967), 129–131.Google Scholar
(7)Mohanty, R. and Mahapatra, S.On the absolute logarithmic summability of a Fourier series. Math. Z. 65 (1956), 207–213.Google Scholar
(8)Mohanty, R. and Misra, B.On absolute logarithmic summability of a sequence related to a Fourier series. Tohoku Math. J. (2), 6 (1954), 5–12.Google Scholar
(9)Mohanty, R. and Ray, B. K.On the summability |R, log | of Fourier series and an associated series. Proc. Cambridge Philos. Soc.. 63 (1967), 721–726.Google Scholar
(10)Mohanty, R. and Ray, B. K.On the convergence factor of a Fourier Series and a differentiated Fourier series. Proc. Cambridge Philos. Soc. 65 (1969), 75–85.Google Scholar
(11)Obrechkoff, N.Sur la sommation des séries trigonométriques de Fourier par less moyennes arithmétiques. Bull. Soc. Math. France 62 (1934), 84–109, 107–184.Google Scholar
(12)Prasad, B. N. and Bhatt, S. N.The summability factors of a Fourier series. Duke. Math. J.. 24 (1957), 103–117.Google Scholar
(13)Varshney, O. P.On the absolute harmonic summability of a series related to a Fourier series. Proc. Amer. Math. Soc.. 10 (1959), 784–789.Google Scholar
(14)Zygmund, A.Trigonometric series p. 253, vol. I (Cambridge, 1959).Google Scholar