Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4620855 | Journal of Mathematical Analysis and Applications | 2008 | 10 Pages |
Abstract
We establish a necessary and sufficient condition for f∈Hp(R), g∈Hq(R) with p−1+q−1⩽1 to satisfy the Bedrosian identity H(fg)=fHg, where H denotes the Hilbert transform. As applications, we prove the Bedrosian theorem for this identity, and give a characterization of f satisfying the identity when g is a finite linear combination of complex sinusoids. We also show that if f is of low Fourier frequency then it is necessary for g to have high Fourier frequency in order to satisfy the Bedrosian identity.
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