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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Continuity and summability for double Fourier series
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by J. J. Gergen and S. B. Littauer PDF
Trans. Amer. Math. Soc. 38 (1935), 401-435 Request permission
References
  • Ralph Palmer Agnew, On Summability of Double Sequences, Amer. J. Math. 54 (1932), no. 4, 648–656. MR 1506927, DOI 10.2307/2371092
  • Ralph Palmer Agnew, On Summability of Multiple Sequences, Amer. J. Math. 56 (1934), no. 1-4, 62–68. MR 1507930, DOI 10.2307/2370913
  • Bosanquet, L. S., On the summability of Fourier series, Proceedings of the London Mathematical Society, vol. 31 (1930), pp. 144-164. —Cesàro summation of Fourier series, ibid., vol. 35 (1934), pp. 17-32. Hardy, G. H., and Littlewood, J. E., Solution of the Cesàro summability problem for power series and Fourier series, Mathematische Zeitschrift, vol. 19 (1923), pp. 67-96. —The allied series of a Fourier series, Proceedings of the London Mathematical Society, vol. 24 (1926), pp. 211-246. Hobson, E. W., Theory of Functions of a Real Variable, Cambridge, vol. I, 1927. —Theory of Functions of a Real Variable, Cambridge, vol. II, 1926. Kogbetliantz, Ervand, Sommation des séries et intégrales divergentes par les moyennes arithmétiques et typiques, Mémorial des Sciences Mathématiques, vol. 51 (1931), pp. 1-84.
  • Florence M. Mears, Riesz summability for double series, Trans. Amer. Math. Soc. 30 (1928), no. 4, 686–709. MR 1501454, DOI 10.1090/S0002-9947-1928-1501454-0
  • Merriman, G. M., Concerning the summability of double series of a certain type, Annals of Mathematics, vol. 28 (1927), pp. 515-533. —A set of necessary and sufficient conditions for Cesàro summability of double series, ibid., vol. 29 (1928), pp. 343-354.
  • Charles N. Moore, On convergence factors in double series and the double Fourier’s series, Trans. Amer. Math. Soc. 14 (1913), no. 1, 73–104. MR 1500937, DOI 10.1090/S0002-9947-1913-1500937-6
  • Paley, R. E. A. C., On the Cesàro summability of Fourier series and allied series, Proceedings of the Cambridge Philosophical Society, vol. 26 (1930), pp. 173-203. Pollard, S., The summation of Denjoy-Fourier series, Proceedings of the London Mathematical Society, vol. 27 (1928), pp. 209-222. Tonelli, L., Serie Trigonometriche, Bologna, 1928.
  • Leonida Tonelli, Su un problema di Abel, Math. Ann. 99 (1928), no. 1, 183–199 (Italian). MR 1512447, DOI 10.1007/BF01459094
  • Wiener, N., A type of Tauberian theorem applying to Fourier series, Proceedings of the London Mathematical Society, 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
  • Young, W. H., On multiple Fourier series, Proceedings of the London Mathematical Society, vol. 11 (1913), pp. 133-184. —On infinite integrals involving a generalization of the sine and cosine functions, Quarterly Journal of Mathematics, vol. 43 (1912), pp. 161-177.
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Additional Information
  • © Copyright 1935 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 38 (1935), 401-435
  • MSC: Primary 42B05; Secondary 42B08
  • DOI: https://doi.org/10.1090/S0002-9947-1935-1501818-9
  • MathSciNet review: 1501818