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Criteria for Fourier transforms

Published online by Cambridge University Press:  09 April 2009

R. E. Edwards
R. E. Edwards
Affiliation:
Institute of Advanced StudiesAustralian National University
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Salem [1] gave the following criterion for Fourier-Lebesgue sequences .

Denote by E the set of continuously differentiate periodic functions u such that u' has an absolutely convergent Fourier series, and let E1 denote the set of uσE satisfying ∥u∥∞≦1.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 7 , Issue 2 , May 1967 , pp. 239 - 246
Copyright
Copyright © Australian Mathematical Society 1967

References

[1]Salem, R., Essais sur les séries trigonométriques, Act. Sci. et Ind., No. 862, Paris (1940).Google Scholar
[2]Rudin, W., Fourier analysis on groups. (Interscience Publishers, New York 1962).Google Scholar
[3]Edwards, R. E., Functional Analysis: Theory and Applications (Holt, Rinehart and Winston, Inc., New York 1965).Google Scholar