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On Density of Fourier Coefficients

Published online by Cambridge University Press:  20 November 2018

Rafat N. Siddiqi
Rafat N. Siddiqi*
Affiliation:
Université De Sherbrooke, Sherbrooke Québec
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Let f be an L integrable real valued function of period 2π and let

(1)

be its Fourier series. It is known that if f is of bounded variation then all nan and nbn(n=1,2,3,…) lie in the interval [-V(F)/π, V(F)/π;] where V(f) is the total variation of f. M. Izumi and S. Izumi [3] have recently asserted the following theorem A about the density of the positive and negative Fourier sine coefficients of a function of bounded variation.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 1 , March 1973 , pp. 93 - 103
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bari, N., A treatise on trigonometric series, Vol. I, Pergamon Press, New York (1964), 210–213.Google Scholar
2. Fejér, L., Über die Bestimmung des Sprunges einer Funktionen aus ihrer Fourierreihe, J. Reine Angew. Math. 142 (1913), 165–168.Google Scholar
3. Izumi, M., and Izumi, S., Fourier coefficients of function of bounded variation, The publications of Ramanujan Institute, Number 1 (1969), 101–106.Google Scholar
4. Siddiqi, J.A., Coefficients properties of certain Fourier series, Math. Ann. 181 (1969), 242–254.Google Scholar
5. Siddiqi, J.A., A strengthened form of a theorem of Fejér, Compositio Math. (3) 21 (1969), 262–270.Google Scholar
6. Zygmund, A., Trigonometric series, Vol. I, Cambridge Univ. Press, New York, 1959.Google Scholar