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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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On the absolute Riesz summability of Fourier series and its conjugate series
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Trans. Amer. Math. Soc. 76 (1954), 351-374 Request permission

Erratum: Trans. Amer. Math. Soc. 77 (1954), 552-552.
References
  • K. Chandrasekharan, The second theorem of consistency for absolutely summable series, J. Indian Math. Soc. (N.S.) 6 (1942), 168–180. MR 8845
  • G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
  • G. H. Hardy and M. Riesz, The general theory of Dirichlet series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 18, 1915.
  • R. Mohanty, A criterion for the absolute convergence of a Fourier series, Proc. London Math. Soc. (2) 51 (1949), 186–196. MR 31097, DOI 10.1112/plms/s2-51.3.186
  • R. Mohanty, On the absolute Riesz summability of Fourier series and allied series, Proc. London Math. Soc. (2) 52 (1951), 295–320. MR 41266, DOI 10.1112/plms/s2-52.4.295
  • N. Obrechkoff, Sur la sommation absolue des séries de Dirichlet, C.R. Acad. Sci. Paris vol. 186 (1928) pp. 215-217.
  • Nikola Obreschkoff, Über die absolute Summierung der Dirichletschen Reihen, Math. Z. 30 (1929), no. 1, 375–386 (German). MR 1545068, DOI 10.1007/BF01187777
  • C. de la Vallée Poussin, Course d’analyse infinitésimale, Louvain-Paris, 1923.
  • Fu Traing Wang, On Riesz summability of Fourier series. III, Proc. London Math. Soc. (2) 51 (1949), 215–231. MR 30636, DOI 10.1112/plms/s2-51.3.215
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Additional Information
  • © Copyright 1954 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 76 (1954), 351-374
  • MSC: Primary 42.4X
  • DOI: https://doi.org/10.1090/S0002-9947-1954-0062260-5
  • MathSciNet review: 0062260