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

DOI:
https://doi.org/10.1090/S0002-9947-1957-0086159-6

MathSciNet review:
0086159

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References | Similar Articles | Additional Information

**[1]**K. Chandrasekharan,*The second theorem of consistency for absolutely summable series*, J. Indian Math. Soc. (N.S.)**6**(1942), 168–180. MR**8845****[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**40458**, https://doi.org/10.1112/jlms/s1-26.2.104**[6]**B. Kuttner,*On the “second theorem of consistency” for Riesz summability. II*, J. London Math. Soc.**27**(1952), 207–217. MR**46459**, https://doi.org/10.1112/jlms/s1-27.2.207**[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**, https://doi.org/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**64889**, https://doi.org/10.1093/qmath/5.1.161**[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**57993**, https://doi.org/10.1112/jlms/s1-29.1.49**[12]**C. de la Vallée Poussin,*Course d'analyse infinitésimale*, (I), Louvain-Paris, 5th ed., 1923.

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DOI:
https://doi.org/10.1090/S0002-9947-1957-0086159-6

Article copyright:
© Copyright 1957
American Mathematical Society