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Biorthogonal Boundary Multiwavelets

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Numerical Mathematics and Advanced Applications ENUMATH 2019

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 139))

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Abstract

The discrete wavelet transform is defined for functions on the entire real line. One way to implement the transform on a finite interval is by using special boundary functions. For orthogonal multiwavelets, this has been studied in previous papers. We describe the generalization of some of these results to biorthogonal multiwavelets.

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References

  1. Altürk, A., Keinert, F.: Regularity of boundary wavelets. Appl. Comput. Harmon. Anal. 32(1), 65–85 (2012)

    Article  MathSciNet  Google Scholar 

  2. Altürk, A., Keinert, F.: Construction of multiwavelets on an interval wavelets. Axioms 2(2), 122–141 (2013)

    Article  Google Scholar 

  3. Andersson, L., Hall, N., Jawerth, B., Peters, G.: Wavelets on closed subsets of the real line. In: Recent advances in wavelet analysis, Wavelet Anal. Appl., vol. 3, pp. 1–61. Academic Press, Boston, MA (1994)

    Google Scholar 

  4. Chui, C.K., Quak, E.: Wavelets on a bounded interval. In: Numerical methods in approximation theory, Vol. 9 (Oberwolfach, 1991), Internat. Ser. Numer. Math., vol. 105, pp. 53–75. Birkhäuser, Basel (1992)

    Google Scholar 

  5. Cohen, A., Daubechies, I., Vial, P.: Wavelets on the interval and fast wavelet transforms. Appl. Comput. Harmon. Anal. 1(1), 54–81 (1993)

    Article  MathSciNet  Google Scholar 

  6. Daubechies, I., Lagarias, J.C.: Two-scale difference equations II: local regularity, infinite products of matrices and fractals. SIAM J. Math. Anal. 23(4), 1031–1079 (1992)

    Article  MathSciNet  Google Scholar 

  7. Jiang, Q.: On the regularity of matrix refinable functions. SIAM J. Math. Anal. 29(5), 1157–1176 (1998)

    Article  MathSciNet  Google Scholar 

  8. Keinert, F.: Wavelets and multiwavelets. Studies in Advanced Mathematics. Chapman & Hall/CRC, Boca Raton, FL (2004)

    Google Scholar 

  9. Yang, S., Cheng, Z., Wang, H.: Construction of biorthogonal multiwavelets. J. Math. Anal. Appl. 276, 1–12 (2002)

    Article  MathSciNet  Google Scholar 

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Correspondence to Fritz Keinert .

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Keinert, F. (2021). Biorthogonal Boundary Multiwavelets. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_57

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