On the Nørlund Summability of a Class of Fourier Series
Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 86-91

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

1. Our aim in this paper is to determine a necessary and sufficient condition for N∅rlund summability of Fourier series and to include a wider class of classical results. A Fourier series, of a Lebesgue-integrable function, is said to be summable at a point by N∅rlund method (N, pn), as defined by Hardy [1], if pn → Σpn → ∞, and the point is in a certain subset of the Lebesgue set. The following main results are known.
Sahney, Badri N. On the Nørlund Summability of a Class of Fourier Series. Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 86-91. doi: 10.4153/CJM-1970-011-3
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[1] 1. Hardy, G. H., Divergent series (Oxford, at the Clarendon Press, 1949). Google Scholar

[2] 2. Hardy, G. H. and Littlewood, J. E., Notes on the theory of series XVIII: On the convergence of Fourier series, Proc. Cambridge Philos. Soc. 31 (1935), 317–323. Google Scholar

[3] 3. Hille, E. and Tamarkin, J. D., On the summability of Fourier series, Trans. Amer. Math. Soc. 84 (1932), 757–783. Google Scholar

[4] 4. Iyengar, K. S. K., A Tauberian theorem and its applications to convergence of Fourier series, Proc. Indian Acad. Sci. Sect. A 18 (1943), 81–87. Google Scholar

[5] 5. Iyengar, K. S. K., New convergence and summability test for Fourier series, Proc. Indian Acad. Sci. Sect. A 18 (1943), 113–120. Google Scholar

[6] 6. Iyengar, K. S. K., Notes on the summability. II. On the relation between summability by Nörlund means of a certain type and summability by Valiron means, Half-Yearly J. Mysore Univ. Sect. B (N.S.) 4 (1944), 161–166. Google Scholar

[7] 7. Jurkat, W., Zur Konvergenztheorie der Fourier-Reihen, Math. Z. 53 (1950-51), 309–339. Google Scholar

[8] 8. Rajagopal, C. T., Nörlund summability of Fourier series, Proc. Cambridge Philos. Soc. 59 (1963), 47–53. Google Scholar

[9] 9. Sahney, B. N., On the (H, p) summability of Fourier series, Boll. Un. Mat. Ital. 16 (1961), 156–163. Google Scholar

[10] 10. Sahney, B. N., On the Nörlund summability of Fourier series, Pacific J. Math. 13 (1963), 251–262. Google Scholar

[11] 11. Siddiqi, J. A., On the harmonic summability of Fourier series, Proc. Indian Acad. Sci. Sect. A 28 (1948), 527–531. Google Scholar

[12] 12. Varshney, O. P., On the relation between harmonic summability and summability by Riesz means of a certain type, Töhoku Math. J. (2) 11 (1959), 20–24. Google Scholar

[13] 13. Varshney, O. P., On the Nörlund summability of Fourier series, Acad. Roy. Belg. Bull. CI. Sci. (5) 52 (1966), 1552–1558. Google Scholar

[14] 14. Wang, F. T., On the Riesz summability of Fourier series, Proc. London Math. Soc. (2) 47 (1942), 308–325. Google Scholar

[15] 15. Zygmund, A., Trigonometrical series, 2nd ed. (Chelsea, New York, 1952). Google Scholar

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