Some arithmetic means connected with Fourier series
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- Trans. Amer. Math. Soc. 39 (1936), 189-204 Request permission
References
-
A. F. Andersen, Studier over Cesàro’s Summabilitetsmetode. Copenhagen, 1921.
L. S. Bosanquet, On Abel’s integral equation and fractional integrals. Proceedings of the London Mathematical Society, (2), vol. 31 (1930), pp. 135-143.
—On the summability of Fourier series. Proceedings of the London Mathematical Society, (2), vol. 31 (1930), pp. 144-164.
—On strongly summable Fourier series. Journal of the London Mathematical Society, vol. 7 (1932), pp. 47-52.
—Note on the limit of a function at a point. Journal of the London Mathematical Society, vol. 7 (1932), pp. 100-105.
—On the Cesàro summation of Fourier series and allied series. Proceedings of the London Mathematical Society, (2), vol. 37 (1934), pp. 17-32.
—The absolute summability (A) of Fourier series. Proceedings of the Edinburgh Mathematical Society, (2), vol. 4 (1934), pp. 12-17.
—Some extensions of Young’s criterion for the convergente of a Fourier series. Quarterly Journal of Mathematics (Oxford series), vol. 6 (1935), pp. 113-123.
L. S. Bosanquet and A. C. Offord, A local property of Fourier series. Proceedings of the London Mathematical Society, (2), vol. 40 (1935), pp. 273-280.
J. J. Gergen, Convergence and summability criteria for Fourier series. Quarterly Journal of Mathematics (Oxford series), vol. 1 (1930), pp. 252-275.
- G. H. Hardy and J. E. Littlewood, Solution of the Cesàro summability problem for power-series and Fourier series, Math. Z. 19 (1924), no. 1, 67–96. MR 1544641, DOI 10.1007/BF01181064 —The allied series of a Fourier series. Proceedings of the London Mathematical Society, (2), vol. 24 (1925), pp. 211-246. —Notes on the theory of series (VII): On Young’s convergence criterion for Fourier series. Proceedings of the London Mathematical Society, (2), vol. 28 (1928), pp. 301-311. —Notes on the theory of series (XVI): Two Tauberian theorems. Journal of the London Mathematical Society, vol. 6 (1931), pp. 281-286. E. W. Hobson, The Theory of Functions of a Real Variable. 2d edition, vol. 2, 1926. E. Kogbetliantz, Sur les séries absolument sommables par la méthode des moyennes arithmétiques. Bulletin des Sciences Mathématiques, (2), vol. 49 (1925), pp. 234-256. —Sommation des Séries et Intégrales Divergentes par les Moyennes Arithmétiques et Typiques. Mémorial des Sciences Mathématiques, vol. 51 (1931). J. E. Littlewood, The converse of Abel’s theorem on power series. Proceedings of the London Mathematical Society, (2), vol. 9 (1910), pp. 434-448. R. E. A. C. Paley, On the Cesàro summability of Fourier series and allied series. Proceedings of the Cambridge Philosophical Society, vol. 26 (1930), pp. 173-203. S. Verblunsky, Note on the sum of oscillating series. Proceedings of the Cambridge Philosophical Society, vol. 26 (1930), pp. 152-157. —On the limit of a function at a point. Proceedings of the London Mathematical Society, (2), vol. 32 (1931), pp. 163-199. N. Wiener, A type of Tauberian theorem applying to Fourier series. Proceedings of the London Mathematical Society, (2), vol. 30 (1929), pp. 1-8.
- Norbert Wiener, Tauberian theorems, Ann. of Math. (2) 33 (1932), no. 1, 1–100. MR 1503035, DOI 10.2307/1968102 W. H. Young, On infinite integrals involving a generalization of the sine and cosine functions. Quarterly Journal of Mathematics, vol. 43 (1912), pp. 161-177. —On the order of magnitude of the coefficients of a Fourier series. Proceedings of the Royal Society, (A), vol. 93 (1916), pp. 42-55. —On the mode of approach to zero of the coefficients of a Fourier series. Proceedings of the Royal Society, (A), vol. 93 (1916), pp. 655-667. —On the convergence of the derived series of a Fourier series. Proceedings of the London Mathematical Society, (2), vol. 17 (1918), pp. 195-236. A. Zygmund, Sur un théorème de M. Gronwall. Bulletin de l’Académie Polonaise (Cracovie), (A), 1925, pp. 207-217.
Additional Information
- © Copyright 1936 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 39 (1936), 189-204
- MSC: Primary 42A24
- DOI: https://doi.org/10.1090/S0002-9947-1936-1501841-5
- MathSciNet review: 1501841