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Determination of jumps for functions based on Malvar-Coifman-Meyer conjugate wavelets

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Abstract

In this paper we discuss determination of jumps for non-periodic function based on Malvar- Cofiman-Meyer (MCM) conjugate wavelets. We prove the equality of Lukacs type. Furthermore we establish several criteria on concentration factors for functions that satisfy weak-smoothness condition of Dini type.

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References

  1. Lukács F. Uber die bestimmung des sprunges einer function aus ihrer Fourierreihe. J Reine Angew Math, 150: 107–122 (1920)

    Google Scholar 

  2. Golubov B I. Determination of the jump of a function of bounded variation by its Fourier series. Math Notes, 12: 444–449 (1975)

    Google Scholar 

  3. Kvernadze G. Determination of the jump of bounded function by its Fourier series. J Approx Theory, 92: 167–190 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Banerjee N S, Geer J. Exponentially accurate approximations to piecewise smooth periodic function. ICASE Report 9s-17, NASA Langley Research Center, 1995

  5. Gelb A, Tadmor E. Determination of edges in spectral data. Appl Comput Harmon Anal, 7: 101–135 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Shi Q L, Shi X L. Determination of jumps in terms of spectral data. Acta Math Hungar, 110: 509–521 (2006)

    Article  Google Scholar 

  7. Zygmund A. Trigonometric Series. Cambridge: Cambridge University Press, 1959

    MATH  Google Scholar 

  8. Hu L, Shi X L. Concentration factors for functions with harmonic bounded mean variation. Acta Math Hungar, 116: 89–103 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Coifman R R, Meyer Y. Remarques sur I, analyse de Fourier á fenêtre. C R Acad Sci Paris, 312: 259–261 (1991)

    MATH  MathSciNet  Google Scholar 

  10. Chui C K, Shi X L. Characterization of biorthogonal Cosine wavelets. J Fourier Anal Appl, 3(5): 559–575 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  11. Bari N K. Trigonometric Series (in Russian). Moscow: Fizmatgiz, 1961

    Google Scholar 

  12. Devore R A, Lorentz G G. Constructive Approximation. Berlin: Springer-Verlag, 1993

    MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Hunan Normal University, Changsha, 410081, China

    XianLiang Shi & Lan Hu

Authors
  1. XianLiang Shi
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  2. Lan Hu
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Corresponding author

Correspondence to XianLiang Shi.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10671062)

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Shi, X., Hu, L. Determination of jumps for functions based on Malvar-Coifman-Meyer conjugate wavelets. Sci. China Ser. A-Math. 52, 443–456 (2009). https://doi.org/10.1007/s11425-008-0100-5

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  • DOI: https://doi.org/10.1007/s11425-008-0100-5

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