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Biorthogonal Bases of Spaces of an n-Separate Multiresolution Analysis and Multiwavelets

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Abstract

We construct biorthogonal bases of spaces of an n-separate multiresolution analysis and wavelets for n scaling functions. Fast algorithms are presented for finding the coefficients of expansions of functions in such bases.

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References

  1. E. A. Pleshcheva, “New generalization of orthogonal wavelet bases,” Proc. Steklov Inst. Math. 273 (Suppl. 1), S124–S132 (2011).

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  2. I. Daubechies, Ten Lectures on Wavelets (SIAM, Philadelphia, 1992; Dinamika, Izhevsk, 2001).

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  3. I. Ya. Novikov, V. Yu. Protasov, and M. A. Skopina, Wavelet Theory (Fizmatlit, Moscow, 2005; Amer. Math. Soc., Providence, RI, 2011).

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990, Russia

    E. A. Pleshcheva

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  1. E. A. Pleshcheva
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Correspondence to E. A. Pleshcheva.

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Original Russian Text © E.A. Pleshcheva, 2016, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Vol. 22, No. 4, pp. 225–232.

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Pleshcheva, E.A. Biorthogonal Bases of Spaces of an n-Separate Multiresolution Analysis and Multiwavelets. Proc. Steklov Inst. Math. 300 (Suppl 1), 145–152 (2018). https://doi.org/10.1134/S0081543818020141

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  • DOI: https://doi.org/10.1134/S0081543818020141

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