Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T12:00:08.607Z Has data issue: false hasContentIssue false
  • English
  • Français

A New Criterion for Borel Summability of Fourier Series

Published online by Cambridge University Press:  20 November 2018

B.N. Sahney  and
P.D. Kathal
B.N. Sahney
Affiliation:
University of Calgary, Alberta
P.D. Kathal
Affiliation:
University of SaugarSaugar, India
Rights & Permissions [Opens in a new window]

Extract

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 application of Borel summability to Fourier series has been discussed by Takahashi and Wang [8] and Sahney [5]. Sahney [6] and Sinvhal [7] obtained sufficient conditions for the Borel summability of the derived Fourier series and its conjugate series, respectively. Kathal [3] obtained different conditions in the case of the conjugate series. In this paper we give a new criterion for Borel summability of Fourier series.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 5 , October 1969 , pp. 573 - 580
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Zygmund, A., Trigonometric series, Vol. 1. (Cambridge University Press, 1959) 55.Google Scholar
2. Hardy, G. H., Divergent series. (Oxford University Press, 1956).Google Scholar
3. Kathal, P.D., Borel summability of derived Fourier series and its conjugate series. Madhya Bharti Jour. of University of Saugar (to appear).Google Scholar
4. Kathal, P.D. and Sahney, B.N., Borel summability of Fourier series. Bolletino Unione Matematica Italiana 3 (1967) 179–182.Google Scholar
5. Sahney, B.H., A note on the Borel summability of Fourier series. Bolletino Unione Matematica Italiana 16 (1961) 44–47.Google Scholar
6. Sahney, B.N., On the Borel summabiiity of the derived Fourier series. Bull. Cal. Math. Soc. 54 (1962) 211–218.Google Scholar
7. Sinvhal, S.D., Borel summabiiity of the conjugate series of a derived series. Duke Math. J. 22 (1955) 445–450.Google Scholar
8. Takahashi, M. and Wang, F. T., On the Borel summabiiity of Fourier series. Pro. Phy. Math. Soc. Japan 18 (1936) 153–156.Google Scholar