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On the Summability of a Class of the Derived Conjugate Series of a 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 2π, and let

1.1

be its Fourier series. The series

1.2

obtained by the term by term differentiation of the series (1. 1), is called the Derived Fourier series of (1. 1). The series conjugate to (1. 2),

1.3

is called the Derived conjugate series of the Fourier series of f.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 5 , October 1965 , pp. 637 - 645
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Hardy, G. H., Divergent series. Oxford, 1949.Google Scholar
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3. Misra, M. L.. Quart. J. Math. 18(1947), pp. 149-51.Google Scholar
4. Mohanty, R. and Nanda, M.. Proc. Amer. Math. Soc., 6 (1955), pp. 594-597.Google Scholar