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Rational orthogonal bases satisfying the Bedrosian identity

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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(ℝ) directly from this family. Moreover, the linear span of the constructed basis is norm dense in L p(ℝ), 1 < p < ∞. Finally, a concrete example of the constructed basis is presented.

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Authors and Affiliations

  1. School of Mathematics and Computer Sciences, Sun-Yat Sen University, Guangzhou, 510275, People’s Republic of China

    Lihui Tan & Lihua Yang

  2. Department of Mathematics, Syracuse University, Syracuse, NY, 13244, USA

    Lixin Shen

Authors
  1. Lihui Tan
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  2. Lixin Shen
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  3. Lihua Yang
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Correspondence to Lixin Shen.

Additional information

Communicated by Yuesheng Xu.

Supported by National Science Foundation of China under grants 60475042 and 10631080.

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Tan, L., Shen, L. & Yang, L. Rational orthogonal bases satisfying the Bedrosian identity. Adv Comput Math 33, 285–303 (2010). https://doi.org/10.1007/s10444-009-9133-8

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  • DOI: https://doi.org/10.1007/s10444-009-9133-8

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