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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The Bedrosian identity for the Hilbert transform of product functions


Authors: Yuesheng Xu and Dunyan Yan
Journal: Proc. Amer. Math. Soc. 134 (2006), 2719-2728
MSC (2000): Primary 65R10
Published electronically: March 23, 2006
MathSciNet review: 2213752
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Abstract: We investigate a necessary and sufficient condition which ensures validity of the Bedrosian identity for the Hilbert transform of a product function $ fg$. Convenient sufficient conditions are presented, which cover the classical Bedrosian theorem and provide us with new insightful information.


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Additional Information

Yuesheng Xu
Affiliation: Department of Mathematics, 215 Carnegie Hall, Syracuse University, Syracuse, New York 13244-1150 – and – Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Email: yxu06@syr.edu

Dunyan Yan
Affiliation: School of Information Science and Engineering, the Graduate School of the Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Email: ydunyan@amss.ac.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08315-8
PII: S 0002-9939(06)08315-8
Keywords: Bedrosian identity, Hilbert transform
Received by editor(s): January 24, 2005
Received by editor(s) in revised form: April 11, 2005
Published electronically: March 23, 2006
Additional Notes: The first author was supported in part by the US National Science Foundation under grant 0407476, by the Natural Science Foundation of China under grant 10371122 and by the Chinese Academy of Sciences under the program “One Hundred Distinguished Young Chinese Scientists”.
Communicated by: David R. Larson
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.