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)

 

 

On the second theorem of consistency in the theory of absolute Riesz summability


Authors: B. N. Prasad and T. Pati
Journal: Trans. Amer. Math. Soc. 85 (1957), 122-133
MSC: Primary 40.0X
MathSciNet review: 0086159
Full-text PDF Free Access

References | Similar Articles | Additional Information

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

  • [1] K. Chandrasekharan, The second theorem of consistency for absolutely summable series, J. Indian Math. Soc. (N.S.) 6 (1942), 168–180. MR 0008845
  • [2] G. H. Hardy, The second theorem of consistency for summable series, Proc. London Math. Soc. (2) vol. 15 (1916) pp. 72-88.
  • [3] G. H. Hardy and M. Riesz, The general theory of Dirichlet's series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 18, 1915.
  • [4] 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.
  • [5] B. Kuttner, Note on the “second theorem of consistency” for Riesz summability, J. London Math. Soc. 26 (1951), 104–111. MR 0040458
  • [6] B. Kuttner, On the “second theorem of consistency” for Riesz summability. II, J. London Math. Soc. 27 (1952), 207–217. MR 0046459
  • [7] N. Obrechkoff, Sur la sommation absolue des séries de Dirichlet, C.R. Acad. Sci. Paris vol. 186 (1928) pp. 215-217.
  • [8] Nikola Obreschkoff, Über die absolute Summierung der Dirichletschen Reihen, Math. Z. 30 (1929), no. 1, 375–386 (German). MR 1545068, 10.1007/BF01187777
  • [9] 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 0064889
  • [10] M. Riesz, Sur les séries de Dirichlet et les séries entières, C.R. Acad. Sci. Paris vol. 149 (1909) pp. 909-912.
  • [11] J. B. Tatchell, A theorem on absolute Riesz summability, J. London Math. Soc. 29 (1954), 49–59. MR 0057993
  • [12] C. de la Vallée Poussin, Course d'analyse infinitésimale, (I), Louvain-Paris, 5th ed., 1923.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 40.0X

Retrieve articles in all journals with MSC: 40.0X


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1957-0086159-6
Article copyright: © Copyright 1957 American Mathematical Society