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Poly-scale refinable function and their properties

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Abstract

Poly-scale refinable function with dilation factor a is introduced. The existence of solution of poly-scale refinable equation is investigated. Specially, necessary and sufficient conditions for the orthonormality of solution function ϕ of poly-scale refinable equation with integer dilation factor a are established. Some properties of poly-scale refinable function are discussed. Several examples illustrating how to use the method to construct poly-scale refinable function are given.

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References

  1. Daubechies I. Orthonormal bases of compactly supported wavelets[J]. Comm Pure Appl Math, 1988, 41(7):909–996.

    MathSciNet  MATH  Google Scholar 

  2. Daubechies I, Lagarias J C. Two-scale difference equations I. Existence and global regularity of solutions[J]. SIAM J Math Anal, 1991, 22(5):1388–1410.

    Article  MathSciNet  MATH  Google Scholar 

  3. Chui C K, Lian Jian-ao. A study on orthonormal multiwavelets[J]. J Appl Numer Math, 1996, 20(3):273–298.

    Article  MathSciNet  MATH  Google Scholar 

  4. Lian J. Orthogonal criteria for multiscaling functions[J]. Appl Comp Harm Anal, 1998, 5(3):277–311.

    Article  MathSciNet  MATH  Google Scholar 

  5. Yang Shouzhi, Cheng Zhengxing, Wang Hongyong. Construction of biorthogonal multiwavelets[J]. J Math Anal Appl, 2002, 276(1):1–12.

    Article  MathSciNet  MATH  Google Scholar 

  6. Yang Shouzhi. A fast algorithm for constructing orthogonal multiwavelets[J]. ANZIAM Journal, 2004, 46(2):185–202.

    MathSciNet  MATH  Google Scholar 

  7. Cabrelli A C, Gordillo M L. Existence of multiwavelets in R n[J]. Proc Amer Math Soc, 2002, 130(5):1413–1424.

    Article  MathSciNet  MATH  Google Scholar 

  8. Dyn N, Levin D. Subdivision schemes in geometric modelling[J]. Acta Numer, 2002, 11(1):73–144.

    Article  MathSciNet  MATH  Google Scholar 

  9. Cohen A, Dyn N, Matei B. Quasilinear subdivision schemes with applications to ENO interpolation[J]. Appl Comput Harmon Anal, 2003, 15(2):89–116.

    Article  MathSciNet  MATH  Google Scholar 

  10. Dekel S, Leviatan D. Wavelet decompositions of nonrefinable shift invariant spaces[J]. Appl Comp Harm Anal, 2002, 12(2):230–258.

    Article  MathSciNet  MATH  Google Scholar 

  11. Blu T, Thvenaz P, Unser M. MOMS: Maximal-order interpolation of minimal support[J]. IEEE Trans Image Process, 2001, 10(7):1069–1080.

    Article  MATH  Google Scholar 

  12. Dekel S, Dyn N. Poly-scale refinablity and subdivision[J]. Appl Comp Harm Anal, 2002, 13(1):35–62.

    Article  MathSciNet  MATH  Google Scholar 

  13. Yang Shouzhi, Yang Xiaozhong. Computation of the support of multiscaling functions[J]. Chinese Journal of Numerical Mathematics and Applications, 2005, 27(2):1–8.

    MathSciNet  MATH  Google Scholar 

  14. Peng Lizhong, Wang Yongge. Parameterization and algebraic structure of 3-band orthogonal wavelet systems[J]. Sci China Ser A, 2001, 44(12):1531–1543.

    Article  MathSciNet  MATH  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou, 515063, Guangdong Province, P. R. China

    Yang Shou-zhi Doctor  (杨守志) (Professor)

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  1. Yang Shou-zhi Doctor  (杨守志)
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Correspondence to Yang Shou-zhi Doctor  (杨守志).

Additional information

Communicated by LI Ji-bin

Project supported by the Natural Science Foundation of Guangdong Province (Nos. 032038, 05008289, 06105648) and the Doctoral Foundation of Guangdong Province (No.04300917)

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Yang, Sz. Poly-scale refinable function and their properties. Appl Math Mech 27, 1687–1695 (2006). https://doi.org/10.1007/s10483-006-1211-1

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  • DOI: https://doi.org/10.1007/s10483-006-1211-1

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Chinese Library Classification

2000 Mathematics Subject Classification

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