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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 second theorem of consistency in the theory of absolute Riesz summability
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by B. N. Prasad and T. Pati PDF
Trans. Amer. Math. Soc. 85 (1957), 122-133 Request permission
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, The second theorem of consistency for summable series, Proc. London Math. Soc. (2) vol. 15 (1916) pp. 72-88. G. H. Hardy and M. Riesz, The general theory of Dirichlet’s series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 18, 1915. K. A. Hirst, On the second theorem of consistency in the theory of summation by typical means, Proc. London Math. Soc. (2) vol. 33 (1932) pp. 353-366.
  • B. Kuttner, Note on the “second theorem of consistency” for Riesz summability, J. London Math. Soc. 26 (1951), 104–111. MR 40458, DOI 10.1112/jlms/s1-26.2.104
  • B. Kuttner, On the “second theorem of consistency” for Riesz summability. II, J. London Math. Soc. 27 (1952), 207–217. MR 46459, DOI 10.1112/jlms/s1-27.2.207
  • 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
  • T. Pati, On the second theorem of consistency in the theory of absolute summability, Quart. J. Math. Oxford Ser. (2) 5 (1954), 161–168. MR 64889, DOI 10.1093/qmath/5.1.161
  • M. Riesz, Sur les séries de Dirichlet et les séries entières, C.R. Acad. Sci. Paris vol. 149 (1909) pp. 909-912.
  • J. B. Tatchell, A theorem on absolute Riesz summability, J. London Math. Soc. 29 (1954), 49–59. MR 57993, DOI 10.1112/jlms/s1-29.1.49
  • C. de la Vallée Poussin, Course d’analyse infinitésimale, (I), Louvain-Paris, 5th ed., 1923.
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Additional Information
  • © Copyright 1957 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 85 (1957), 122-133
  • MSC: Primary 40.0X
  • DOI: https://doi.org/10.1090/S0002-9947-1957-0086159-6
  • MathSciNet review: 0086159