Rational orthogonal bases satisfying the Bedrosian identity

Authors:
Lihui Tan;Lixin Shen;Lihua Yang
Affiliations:
School of Mathematics and Computer Sciences, Sun-Yat Sen University, Guangzhou, People's Republic of China 510275;Department of Mathematics, Syracuse University, Syracuse, USA 13244;School of Mathematics and Computer Sciences, Sun-Yat Sen University, Guangzhou, People's Republic of China 510275
Venue:
Advances in Computational Mathematics
Year:
2010

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Abstract

We develop a necessary and sufficient condition for the Bedrosian identity in terms of the boundary values of functions in the Hardy spaces. This condition allows us to construct a family of functions such that 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(驴) directly from this family. Moreover, the linear span of the constructed basis is norm dense in L p (驴), 1驴p驴