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On the summability of Fourier series. I


Authors: Einar Hille and J. D. Tamarkin
Journal: Trans. Amer. Math. Soc. 34 (1932), 757-783
MSC: Primary 42A24
DOI: https://doi.org/10.1090/S0002-9947-1932-1501662-X
MathSciNet review: 1501662
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  • [1] G. C. Evans, Complements of potential theory, American Journal of Mathematics, vol. 54 (1932), pp. 213-234. MR 1506886
  • [2] G. H. Hardy, Theorems relating to the summability and convergence of slowly oscillating series, Proceedings of the London Mathematical Society, (2), vol. 8 (1910), pp. 301-320.
  • [3] G. H. Hardy, The summability of a Fourier series by logarithmic means, Quarterly Journal of Mathematics (Oxford series), vol. 2 (1931), pp. 107-112.
  • [4] E. Hille and J. D. Tamarkin, On the summability of Fourier series, Proceedings of the National Academy of Sciences, vol. 14 (1928), pp. 915-918.
  • [5] D. S. Morse, Relative inclusiveness of certain definitions of summability, American Journal of Mathematics, vol. 45 (1923), pp. 259-285. MR 1506508
  • [6] N. E. Nörlund, Sur une application des fonctions permutables, Lunds Universitets Årsskrift, (N.F.), avd. 2, 16, No. 3 (1920); 10 pp.
  • [7] M. Riesz, Sur l'équivalence de certaines méthodes de sommation, Proceedings of the London Mathematical Society, (2), vol. 22 (1924), pp. 412-419.
  • [8] G. F. Woronoi, Extension of the notion of the limit of the sum of terms of an infinite series (in Russian). Proceedings of the Eleventh Congress (1901) of Russian Naturalists and Physicians, St. Petersburg, 1902, pp. 60-61. Annotated English translation by J. D. Tamarkin, Annals of Mathematics, (2), vol. 33 (1932), pp. 422-428. MR 1503066

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DOI: https://doi.org/10.1090/S0002-9947-1932-1501662-X
Article copyright: © Copyright 1932 American Mathematical Society

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