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Pointwise Convergence of Trigonometric Series

Part of: Harmonic analysis in one variable

Published online by Cambridge University Press:  09 April 2009

Chang-Pao Chen
Chang-Pao Chen
Affiliation:
Department of MathematicsStanford UniversityStanford, California 94305, U.S.A.
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We establish two results in the pointwise convergence problem of a trigonometric series for some nonnegative integer m. These results not only generalize Hardy's theorem, the Jordan test theorem and Fatou's theorem, but also complement the results on pointwise convergence of those Fourier series associated with known L1-convergence classes. A similar result is also established for the case that , where {ln} satisfies certain conditions.

Keywords

pointwise convergence of a trigonometric seriesFourier series.

MSC classification

Secondary: 42A20: Convergence and absolute convergence of Fourier and trigonometric series 42A32: Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 3 , December 1987 , pp. 291 - 300
Copyright
Copyright © Australian Mathematical Society 1987

References

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