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WAVELET FRAMES WITH MATCHED MASKS

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Abstract

In the paper, we design a Parseval wavelet frame with a compact support and many vanishing moments. The corresponding refinement mask approximates an arbitrary continuous periodic function f, \(f(0)=1\). The refinable function has stable integer shifts.

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References

  1. Bownik, M.: Connectivity and density in the set of framelets Math. Res. Lett. 14 (2007), 285–293.

  2. Cabrelli, C. , Molter, U.M.: “Density of the Set of Generators of Wavelets Systems”, Constructive Approximation, 26 (1) (2007).

  3. Chui, C., He, W.: Compactly supported tight frames associated with refinable functions. Appl. Comput. Harmon. Anal. 8, 293–319 (2000)

  4. Daubechies, I., Han, B., Ron, A., Shen, Z.: Framelets: MRA-based constructions of wavelet frames. Appl. Comp. Harm. Anal. 14(1), 1–46 (2003).

  5. R. Larson, Von Neumann algebras and wavelets. Operator algebras and applications (Samos, 1996), 267-312, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 495, Kluwer Acad. Publ., Dordrecht, 1997.

  6. I. Ya. Novikov, V. Yu. Protasov, and M. A. Skopina Wavelet Theory, Translations of Mathematical Monographs 239 (AMS, Providence), 2011.

  7. Petukhov, A.: Explicit construction of framelets. Appl. Comput. Harmon. Anal. 11, 313–327 (2001)

  8. Ron, A., Shen, Z.: Affine systems in \(L_{2}(\mathbb{R}^{d})\): the analysis of the analysis operator. J. Funct. Anal. 148, 408–447 (1997).

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Funding

The work is supported by the Russian Science Foundation (grant 18-11-00055).

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Authors and Affiliations

  1. Mathematics and Mechanics Faculty, Saint Petersburg State University, Universitetsky prospekt, 28, Saint Petersburg, 198504, Peterhof, Russia

    Elena A. Lebedeva

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  1. Elena A. Lebedeva
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Correspondence to Elena A. Lebedeva.

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Lebedeva, E.A. WAVELET FRAMES WITH MATCHED MASKS. J Math Sci 266, 886–891 (2022). https://doi.org/10.1007/s10958-022-06147-6

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  • DOI: https://doi.org/10.1007/s10958-022-06147-6

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