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Necessary and sufficient type theorem for absolute Nörlund summability of conjugate series


Author: Arun Kumar
Journal: Proc. Amer. Math. Soc. 67 (1977), 77-83
MSC: Primary 42A28; Secondary 40D15, 40F05
DOI: https://doi.org/10.1090/S0002-9939-1977-0510923-8
MathSciNet review: 0510923
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Abstract: Sufficient conditions for $ \vert N,{p_n}\vert$ summability of the conjugate series of Fourier series have been obtained earlier. The author obtains here a set of necessary and sufficient conditions for the result. This improves earlier results and provides a unified version of them.


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

  • [1] L. S. Bosanquet and J. M. Hyslop, On the absolute summability of the allied series of a Fourier series, Math. Z. 42 (1937), 489-512. MR 1545688
  • [2] H. P. Dikshit, On a class of Nörlund means and Fourier series, Pacific J. Math. 33 (1970), 559-569. MR 0267343 (42:2245)
  • [3] H. P. Dikshit and A. Kumar, Absolute summability of Fourier series with factors, Pacific J. Math. 61 (1975), 59-69. MR 0404970 (53:8768)
  • [4] B. Kuttner and B. N. Sahney, On the absolute matrix summability of Fourier series, Pacific J. Math. 43 (1972), 407-419. MR 0320611 (47:9147)
  • [5] R. Mohanty, The absolute Cesàro summability of some series associated with a Fourier series and its allied series, J. London Math. Soc. 25 (1950), 63-67. MR 0034467 (11:592c)
  • [6] T. Pati, On the absolute Nörlund summability of the conjugate series of a Fourier series, J. London Math. Soc. 38 (1963), 204-214. MR 0149193 (26:6685)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0510923-8
Keywords: Absolute summability, Nörlund mean, Fourier series, allied series
Article copyright: © Copyright 1977 American Mathematical Society

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