Abstract
We characterize a class of functions satisfying the classical Bedrosian identity or the circular Bedrosian identity by certain homogeneous semi-convolution equations. The structure of solutions of these equations is then studied using translation invariant subspaces of Hardy spaces and additive positive definite kernels. The obtained results provide some insight into the Bedrosian identity and a construction of intrinsic mode functions for the time-frequency analysis of nonlinear and nonstationary signals.
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