Geodesic
A New Criterion for Borel Summability of Fourier Series
Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 573-580

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Sahney, B.N.; Kathal, P.D. A New Criterion for Borel Summability of Fourier Series. Canadian mathematical bulletin, Tome 12 (1969) no. 5, pp. 573-580. doi: 10.4153/CMB-1969-074-x
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[1] 1. Zygmund, A., Trigonometric series, Vol. 1. (Cambridge University Press, 1959) 55. Google Scholar

[2] 2. Hardy, G. H., Divergent series. (Oxford University Press, 1956). Google Scholar

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[7] 7. Sinvhal, S.D., Borel summabiiity of the conjugate series of a derived series. Duke Math. J. 22 (1955) 445–450. Google Scholar

[8] 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

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