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Bedrosian Identity in Blaschke Product Case

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Abstract

This paper offers a characterization of amplitude functions in \({L^2(\mathbb R)}\) satisfying the Bedrosian identity in the case that the phase functions are determined by the boundary value on the unit circle of finite Blaschke products.

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References

  1. Bedrosian E.: A product theorem for Hilbert transform. Proc. IEEE 51, 868–869 (1963)

    Article  Google Scholar 

  2. Boashash B.: Estimating and interpreting the instantaneous frequency of a signal. I. Fundamentals. Proc. IEEE 80, 417–430 (1992)

    Google Scholar 

  3. Cerejeiras P., Chen Q., Kaehler U.: A necessary and sufficient condition for the Bedrosian identity. Math. Method Appl. Sci. 33(4), 373–562 (2010)

    Google Scholar 

  4. Nuttall A.H.: On the quadrature approximation to the Hilbert transform of modulated signals. Proc. IEEE 54, 1458–1459 (1966)

    Article  Google Scholar 

  5. Picinbono B.: On instantaneous amplitude and phase of signals. IEEE Trans. Signal Process. 45(3), 552–560 (1997)

    Article  MathSciNet  Google Scholar 

  6. Qian T.: Characterization of boundary values of functions in Hardy spaces with applications in signal analysis. J. Integral Equ. Appl. 17(2), 159–198 (2005)

    Article  MATH  Google Scholar 

  7. Qian T., Xu Y., Yan D., Yu B.: Fourier spectrum characterization of Hardy spaces and applications. Proc. Am. Math. Soc. 137(3), 971–980 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Yu B., Zhang H.: The Bedrosian identity and homogeneous semi-convolution equations. J. Integral Equ. Appl. 20(4), 527–568 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Paula Cerejeiras, Qiuhui Chen & Uwe Kaehler

  2. School of Informatics, Guangdong University of Foreign Studies, Guangzhou, People’s Republic of China

    Qiuhui Chen

Authors
  1. Paula Cerejeiras
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  2. Qiuhui Chen
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  3. Uwe Kaehler
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Corresponding author

Correspondence to Uwe Kaehler.

Additional information

Communicated by Daniel Aron Alpay.

P. Cerejeiras was supported by Unidade de Investigação Matemática e Aplicações of the University of Aveiro. Q. Chen was supported by NSF of Guangdong Province (Project No. 8151042001000005), the National Research Foundation for the Doctoral Program of Higher Education of China (SRFDP) under grant 20070512001, and is recipient of the Research Position C2007-UA/MAT.APLIC/01. U. Kaehler was supported by Unidade de Investigação Matemática e Aplicações of the University of Aveiro.

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Cerejeiras, P., Chen, Q. & Kaehler, U. Bedrosian Identity in Blaschke Product Case. Complex Anal. Oper. Theory 6, 275–300 (2012). https://doi.org/10.1007/s11785-010-0092-3

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  • DOI: https://doi.org/10.1007/s11785-010-0092-3

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