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On a sequence of Fourier coefficients

Published online by Cambridge University Press:  17 April 2009

V. Venu Gopal Rao  and
B.N. Sahney
V. Venu Gopal Rao
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT;
B.N. Sahney
Affiliation:
Department of Mathematics, Statistics and Computer Science, The University of Calgary, Alberta, Canada.
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Abstract

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In this paper we establish (c, 1) summability of the sequence {nBn (x)} and by using Tauber's Second Theorem, we deduce the convergence criterion of the conjugate series of a Fourier series.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 3 , December 1971 , pp. 343 - 349
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Mohanty, R. and Nanda, M., “On the behavior of Fourier coefficients”, Proc. Amer. Math. Soc. 5 (1954), 79–84.CrossRefGoogle Scholar
[2]Obrechkoff, N., “Sur la série conjugée de la série de Fourier”, Annuaire [Godišnik] Univ. Sofia, Fac. Phys.-Math. Livre 1, 39 (1943), 321–380.Google Scholar
[3]Zygmund, Antoni, Trigonometrical series (Monografie Matematyczne, Tom 5. Warszawa - Lwow, 1935).Google Scholar