Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-23T03:03:55.785Z Has data issue: false hasContentIssue false
  • English
  • Français

Absolute Nörlund summability of Fourier series of functions of bounded variation

Published online by Cambridge University Press:  17 April 2009

Masako Izumi  and
Shin-ichi Izumi
Masako Izumi
Affiliation:
Institute of Advanced Studies, Australian National University, Canberra, ACT.
Shin-ichi Izumi
Affiliation:
Institute of Advanced Studies, Australian National University, Canberra, ACT.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The authors prove two theorems. The first theorem generalizes theorems due to T. Singh and O.P. Varshney, concerning absolute Nörlund summability of Fourier series of functions of bounded variation. The second theorem generalizes theorems of L.S. Bosanquet and H.P. Dikshit.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 1 , August 1970 , pp. 111 - 123
Copyright
Copyright © Australian Mathematical Society 1970

References

[1] Singh, Tarkeshwar, “Absolute Nörlund summability of Fourier series”, Indian J. Math. 6 (1964), 129–136.Google Scholar
[2] Pati, T., “On the absolute Nörlund summability of a Fourier series”, J. London Math. Soc. 34 (1959), 153–160. “Addendum: On the absolute Nörlund summability of a Fourier series”, J. London Math. Soc. 37 (1962), 256.CrossRefGoogle Scholar
[3] Dikshit, H.P., “Absolute summability of a Fourier series by Nörlund means”, Math. Z. 102 (1967), 166–170.Google Scholar
[4] Varshney, O.P., “On the absolute Nörlund summability of a Fourier series”, Math. Z. 83 (1964), 18–24.Google Scholar
[5] Varshney, O.P., “On the absolute summability of Fourier series by a Nörlund method”, Univ. Roorkee Res. J. 6 (1963), 103–113.Google Scholar
[6] Pati, T., “The non-absolute summability of Fourier series by a Nörlund method”, Indian M. Math. 25 (1961), 197–214.Google Scholar
[7] Mohanty, R. and Ray, B.K., “On the non-absolute summability of a Fourier series and the conjugate of a Fourier series by a Nörlund method”, Proc. Cambridge Philos. Soc. 63 (1967), 407–411.Google Scholar
[8] Hille, Einar and Tamarkin, J.D., “On the summability of Fourier series I”, Trans. Amer. Math. Soc. 34 (1932), 757–783.CrossRefGoogle Scholar
[9] McFadden, Leonard, “Absolute Nörlund summability”, Duke Math. J. 9 (1942), 168–207.CrossRefGoogle Scholar
[10] Zygmund, A., Trigonometric series (Cambridge University Press, 2nd ed., Vol. 1, New York, 1959).Google Scholar
[11] Bosanquet, L.S., “The absolute Cesàro summability of a Fourier series”, Proc. London Math. Soc. (2) 41 (1936), 517–528.CrossRefGoogle Scholar
[12] Dikshit, H.P., “Absolute (C, 1)-(N, pn ) summability of a Fourier series and its conjugate series”, Pacific J. Math. 26 (1968), 245–256.CrossRefGoogle Scholar