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On the Summability of a Class of Derived Fourier Series

Published online by Cambridge University Press:  20 November 2018

Narendra K. Govil
Narendra K. Govil*
Affiliation:
University of Montreal
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Let f(t) be integrable L(-π, π) and periodic with period 2 π and let

1.1

be its Fourier series. The series

1.2

obtained by term by term differentiation of the series (1.1) is called the derived Fourier series of f.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 1 , April 1967 , pp. 79 - 84
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Hardy, G. H., Divergent series. Oxford (1944).Google Scholar
2. Peterson, G. M., On the summability of a class of Fourier series. Proc, Amer. Math. Soc. 11 (1960), pages 994-998.Google Scholar
3. Mohanty, R. and Nanda, M., Note on the first Cesaro mean of the derived Fourier series. Proc. Amer. Math. Soc. 5 (1955), pages 566-570.Google Scholar