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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

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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