Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

 

 

Continuity and summability for double Fourier series


Authors: J. J. Gergen and S. B. Littauer
Journal: Trans. Amer. Math. Soc. 38 (1935), 401-435
MSC: Primary 42B05; Secondary 42B08
MathSciNet review: 1501818
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] Ralph Palmer Agnew, On Summability of Double Sequences, Amer. J. Math. 54 (1932), no. 4, 648–656. MR 1506927, 10.2307/2371092
  • [2] Ralph Palmer Agnew, On Summability of Multiple Sequences, Amer. J. Math. 56 (1934), no. 1-4, 62–68. MR 1507930, 10.2307/2370913
  • [3] Bosanquet, L. S., On the summability of Fourier series, Proceedings of the London Mathematical Society, vol. 31 (1930), pp. 144-164.
  • [4] -Cesàro summation of Fourier series, ibid., vol. 35 (1934), pp. 17-32.
  • [5] 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.
  • [6] -The allied series of a Fourier series, Proceedings of the London Mathematical Society, vol. 24 (1926), pp. 211-246.
  • [7] Hobson, E. W., Theory of Functions of a Real Variable, Cambridge, vol. I, 1927.
  • [8] -Theory of Functions of a Real Variable, Cambridge, vol. II, 1926.
  • [9] Kogbetliantz, Ervand, Sommation des séries et intégrales divergentes par les moyennes arithmétiques et typiques, Mémorial des Sciences Mathématiques, vol. 51 (1931), pp. 1-84.
  • [10] Florence M. Mears, Riesz summability for double series, Trans. Amer. Math. Soc. 30 (1928), no. 4, 686–709. MR 1501454, 10.1090/S0002-9947-1928-1501454-0
  • [11] Merriman, G. M., Concerning the summability of double series of a certain type, Annals of Mathematics, vol. 28 (1927), pp. 515-533.
  • [12] -A set of necessary and sufficient conditions for Cesàro summability of double series, ibid., vol. 29 (1928), pp. 343-354.
  • [13] 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, 10.1090/S0002-9947-1913-1500937-6
  • [14] 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.
  • [15] Pollard, S., The summation of Denjoy-Fourier series, Proceedings of the London Mathematical Society, vol. 27 (1928), pp. 209-222.
  • [16] Tonelli, L., Serie Trigonometriche, Bologna, 1928.
  • [17] Leonida Tonelli, Su un problema di Abel, Math. Ann. 99 (1928), no. 1, 183–199 (Italian). MR 1512447, 10.1007/BF01459094
  • [18] Wiener, N., A type of Tauberian theorem applying to Fourier series, Proceedings of the London Mathematical Society, vol. 30 (1929), pp. 1-8.
  • [19] Norbert Wiener, Tauberian theorems, Ann. of Math. (2) 33 (1932), no. 1, 1–100. MR 1503035, 10.2307/1968102
  • [20] Young, W. H., On multiple Fourier series, Proceedings of the London Mathematical Society, vol. 11 (1913), pp. 133-184.
  • [21] -On infinite integrals involving a generalization of the sine and cosine functions, Quarterly Journal of Mathematics, vol. 43 (1912), pp. 161-177.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42B05, 42B08

Retrieve articles in all journals with MSC: 42B05, 42B08


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1935-1501818-9
Article copyright: © Copyright 1935 American Mathematical Society