Journal of University of Chinese Academy of Sciences >
Bedrosian identity for two classes of distribution
Received date: 2008-11-07
Revised date: 2009-02-19
Online published: 2009-07-15
We investigate the Hilbert transform of the products of the integral functions and two classes of distribution: polynomial and exponential functions. A sufficient condition and a sufficient and necessary condition for the Bedrosian identity are presented.
Key words: Hilbert transform; distribution; Bedrosian identity
TONG Zheng-Qing , WANG Rui , YAN Dun-Yan . Bedrosian identity for two classes of distribution[J]. Journal of University of Chinese Academy of Sciences, 2009 , 26(4) : 433 -437 . DOI: 10.7523/j.issn.2095-6134.2009.4.001
[1] Bedrosian E. A product theorem for Hilbert transforms
[J].Proc IEEE,1963,51:868-869.
[2] Brown J L.Analytic signals and product theorems for Hilbert transforms
[J].IEEE Trans Circuits and Systems,1974,CAS-21:790-792.
[3] Cain G D.Hilbert transform relations for products
[J].Proc IEEE,1973,61:663-664.
[4] Qian T,Xu Y S,Yan D Y,et al.Fourier spectrum characterization of Hardy spaces and applications
[J]. Proc Amer Math Soc,2009,137(3):971-980.
[5] Xu Y S,Yan D Y. The Hilbert transform of product functions and the Bedrosian identity
[J]. Proc Amer Math Soc,2006,134:2719-2728.
[6] Yu B,Zhang H Z. The Bedrosian identity and homogeneous semiconvolution equations
[J]. J Integral Equations Appl,2008,20(4):527-568.
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