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Transactions of the American Mathematical Society

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Circular summability $ C$ of double trigonometric series


Author: Victor L. Shapiro
Journal: Trans. Amer. Math. Soc. 76 (1954), 223-233
MSC: Primary 42.4X
DOI: https://doi.org/10.1090/S0002-9947-1954-0061688-7
MathSciNet review: 0061688
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References [Enhancements On Off] (What's this?)

  • [1] S. Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc. vol. 40 (1936) pp. 175-207. MR 1501870
  • [2] M. T. Cheng, On a theorem of Nicolesco and generalized Laplace operators, Proc. Amer. Math. Soc. vol. 2 (1951) pp. 77-85. MR 0041292 (12:825f)
  • [3] R. Courant and D. Hilbert, Methoden der mathematischen Physik II, Berlin, 1937.
  • [4] G. H. Hardy, The second theorem of consistency for summable series, Proc. London Math. Soc. (2) vol. 15 (1916) pp. 72-88.
  • [5] M. Nicolesco, Les fonctions polyharmoniques, Exposés sur la théorie des fonctions, vol. 4, 1936, Paris.
  • [6] G. N. Watson, Theory of Bessel functions, Cambridge, 1944.
  • [7] A. Zygmund, Trigonometrical series, Warsaw, 1935.

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DOI: https://doi.org/10.1090/S0002-9947-1954-0061688-7
Article copyright: © Copyright 1954 American Mathematical Society

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