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A Tauberian theorem for the $ (C,\,1)(N,\,1/(n+1))$ summability method

Author: H. P. Dikshit
Journal: Proc. Amer. Math. Soc. 25 (1970), 391-392
MSC: Primary 40.42
MathSciNet review: 0267314
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Abstract: A Tauberian theorem is proved which infers the $ (C,1)$ summability of a sequence associated with a formally differential Fourier series from its $ (C,1)(N,1/(n + 1))$ summability under suitable conditions.

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

  • [1] G. Das, Tauberian theorems for absolute Nörlund summability, Proc. London Math. Soc. (3) 19 (1969), 357-384. MR 0240503 (39:1850)
  • [2] H. P. Dikshit, Summability of a sequence of Fourier coefficients by a triangular matrix transformation, Proc. Amer. Math. Soc. 21 (1969), 10-20. MR 0254501 (40:7709)
  • [3] K. S. K. Iyengar, A Tauberian theorem and its application to convergence of Fourier series, Proc. Indian Acad. Sci. Sect. A 18 (1943), 81-87. MR 5, 65. MR 0008857 (5:65e)

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Keywords: Product matrix, Tauberian theorem
Article copyright: © Copyright 1970 American Mathematical Society

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