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On the Integral Modulus of Continuity of Fourier Series

Part of: Harmonic analysis in one variable

Published online by Cambridge University Press:  09 April 2009

Babu Ram  and
Suresh Kumari
Babu Ram
Affiliation:
Department of MathematicsMaharshi Dayanand UniversityRohtak-124001, India
Suresh Kumari
Affiliation:
Department of MathematicsMaharshi Dayanand UniversityRohtak-124001, India
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Abstract

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For a wide class of sine trigonometric series we obtain an estimate for the integral modulus of continuity.

MSC classification

Secondary: 42A32: Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 2 , April 1988 , pp. 151 - 158
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Aljančić, S., ‘Sur le module des séries de Fourier particuliéres et sur le module des séries de Fourier transformees par des types divers’, Bull. Acad. Serbe Sci. Arts 30 (6) (1967), 13–38.Google Scholar
[2]Izumi, M., and Izumi, S., ‘Modulus of continuity of functions defined by trigonometric series’, J. Math. Anal. Appl. 24 (1968), 564–581.CrossRefGoogle Scholar
[3]Ram, B., ‘On the integral modulus of continuity of Fourier series’, J. Analyse Math. 28 (1975), 78–85.CrossRefGoogle Scholar
[4]Ram, B., ‘Convergence of certain cosine sums in the metric space L’, Proc. Amer. Math. Soc. 66 (1977), 258–260.Google Scholar
[5]Teljakovsk, S. A., ‘The integral modulus of continuity of functions with quasiconvex Fourier coefficients’, Sibirsk. Mat. Ž. 11 (1970), 1140–1145.Google Scholar
[6]Teljakovski, S. A., ‘A sufficient condition of Sidon for the integrability of trigonometric series’, Mat. Zametki 14 (1973), 317–328.Google Scholar
[7]Timan, A. F., Theory of approximation of functions of ral variables (Hindustan Publishing Corporation, India, 1966).Google Scholar