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Courant type approximations and their wavelet decomposition

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Abstract

Courant type functions (not necessarily piecewise linear) are considered, and a wavelet decomposition of the corresponding embedded spaces is constructed. Model examples are presented. Bibliography: 9 titles. Illustrations: 2 figures.

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References

  1. S. Mallat, A Wavelet Tour of Signal Processing, Acad. Press, 1999.

  2. I. Ya. Novikov, V. Yu. Protasov, and M. A. Skopina, Wavelet Theory [in Russian], Fizmatlit, Moscow, 2005.

    Google Scholar 

  3. I. E. Maksimenko and M. A. Skopina, “Multidimensional periodic wavelets” [in Russian], Algebra Anal. 15 (2003), no. 2, 1–39; English transl.: St. Petersb. Math. J. 15 (2004), no. 2, 165–190.

    MathSciNet  Google Scholar 

  4. J. Maes and A. Bultheel, “Stability analysis of biorthogonal multiwavelets whose duals are not in L 2 and its application to local semiorthogonal lifting,” Appl. Numer. Math. (2007). doi:10.1016/j.apnum.2007.03.002.

  5. Yu. K. Dem’yanovich, Local Approximation on a Manifold and Minimal Splines [in Russian], St. Petersb. Univ. Press, St. Petersburg, 1994.

    MATH  Google Scholar 

  6. Yu. K. Dem’yanovich and A. V. Zimin, “Wavelet decompositions on a manifold” [in Russian], Zap. Nauchn. Semin. POMI 346 (2007), 1–13.

    Google Scholar 

  7. Yu. K. Dem’yanovich, “Spline-wavelet decompositions on manifolds” [in Russian], Probl. Mat. Anal. 36 (2007), 15–22; English transl.: J. Math. Sci., New York 150 (2008), no. 1, 1787–1798.

    Google Scholar 

  8. Yu. K. Dem’yanovich, “A local wavelet basis on an irregular grid” [in Russian], Zap. Nauchn. Semin. POMI 334 (2006), 84–110; English transl.: J. Math. Sci., New York 141 (2007), no.6, 1618–1632.

    MATH  Google Scholar 

  9. A. A. Makarov “On an algebraic identity in the theory of {ie022-01}-splines of second order” [in Russian], Vest. S. Peterburg. State Univ., Ser. 1 (2007), no. 1, 96–98.

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Correspondence to Yu. K. Dem’yanovich.

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Translated from Problemy Matematicheskogo Analiza, No. 37, 2008, pp. 3–22.

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Dem’yanovich, Y.K., Zimin, A.V. Courant type approximations and their wavelet decomposition. J Math Sci 154, 1–22 (2008). https://doi.org/10.1007/s10958-008-9150-z

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  • DOI: https://doi.org/10.1007/s10958-008-9150-z

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