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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0267314-0
MathSciNet review:
0267314
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Abstract | References | Similar Articles | Additional Information
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.
- G. Das, Tauberian theorems for absolute Nörlund summability, Proc. London Math. Soc. (3) 19 (1969), 357–384. MR 240503, DOI https://doi.org/10.1112/plms/s3-19.2.357
- H. P. Dikshit, Summability of a sequence of Fourier coefficients by a triangular matrix transformation, Proc. Amer. Math. Soc. 21 (1969), 10–20. MR 254501, DOI https://doi.org/10.1090/S0002-9939-1969-0254501-2
- 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 0008857
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Additional Information
Keywords:
Product matrix,
Tauberian theorem
Article copyright:
© Copyright 1970
American Mathematical Society