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Rational orthogonal bases satisfying the Bedrosian identity. (English) Zbl 1204.30045

Summary: We develop a necessary and sufficient condition for the Bedrosian identity in terms of the boundary values of functions in Hardy spaces. This condition allows us to construct a family of functions, each of which has non-negative instantaneous frequency, and is the product of two functions satisfying the Bedrosian identity. We then provide an efficient way to construct orthogonal bases of \(L^2(\mathbb R)\) directly from this family. Moreover, the linear span of the constructed basis is norm dense in \(L^p(\mathbb R)\), \(1<p<\infty\). Finally, a concrete example of the constructed basis is presented.

MSC:

30H10 Hardy spaces
46E20 Hilbert spaces of continuous, differentiable or analytic functions

Citations:

Zbl 0435.30001
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Full Text: DOI

References:

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