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

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References

  1. Bosanquet, L. S.: The summability of Laplace-Stieltjes integrals. Proc. London Math. Soc. (3),3, 267–304 (1953).

    Google Scholar 

  2. Chandrasekharan, K.: The second theorem of consistency for absolutely summable series. J. Indian Math. Soc. (New Series)6, 168–180 (1942).

    Google Scholar 

  3. Guha, U.: The “second theorem of consistency” for absolute Riesz summability. J. London Math. Soc.31, 300–311 (1956).

    Google Scholar 

  4. Hardy, G. H.: The second theorem of consistency for summable series. Proc. London Math. Soc. (2),15, 72–88 (1916).

    Google Scholar 

  5. Hardy, G. H., andM. Riesz: The general theory of Dirichlet's series. Cambridge Tracts in Maths. and Math. Physics, No. 18 (1915).

  6. Knopp, K., andG. G. Lorentz: Beiträge zur absoluten Limitierung. Arch. Math.2, 10–16 (1949).

    Google Scholar 

  7. Obrechkoff, N.: Sur la sommation absolue des séries de Dirichlet. C. R. Acad. Sci. (Paris)186, 215–217 (1928).

    Google Scholar 

  8. Obrechkoff, N.: Über die absolute Summierung der Dirichletschen Reihen. Math. Z.30, 375–386 (1929).

    Google Scholar 

  9. Pati, T.: On the second theorem of consistency in the theory of absolute summability. Quart. J. Math. (Oxford Ser.) (2),5, 161–168 (1954).

    Google Scholar 

  10. Pati, T.: Contributions to the study of absolute summability of series. Thesis (D. Sc.), Allahabad University (1956).

  11. Prasad, B. N., andT. Pati: On the second theorem of consistency in the theory of absolute Riesz summability. Trans. Amer. Math. Soc.85, 122–133 (1957).

    Google Scholar 

  12. Prasad, B. N., andT. Pati: On the theorems of consistency for absolute Riesz summability. Read before the Indian Science Congress, January, 1956, and abstracted in the Proceedings.

  13. Riesz, M.: Sur les séries de Dirichlet et les séries entières. C. R. Acad. Sci. (Paris)149, 909–912 (1909).

    Google Scholar 

  14. Tatchell, J. B.: A theorem on absolute Riesz summability. J. London Math. Soc.29, 49–59 (1954).

    Google Scholar 

  15. de la Vallée Poussin, C.: Course d'analyse infinitésimale (I), Louvain-Paris, 5th Ed. (1923).

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  1. Allahabad, India

    B. N. Prasad & T. Pati

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  1. B. N. Prasad
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  2. T. Pati
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Prasad, B.N., Pati, T. The second theorem of consistency in the theory of absolute Riesz summability. Math. Ann. 140, 187–197 (1960). https://doi.org/10.1007/BF01361144

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