Sufficient conditions for a trigonometric polynomial to be a refinement mask corresponding to a tight wavelet frame are obtained. The condition is formulated in terms of the roots of a mask. In particular, it is proved that any trigonometric polynomial can serve as a mask if its associated algebraic polynomial has only negative roots (of course at least one of them equals −1).
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References
A. Ron and Z. Shen, “Affine systems in L2(ℝd): the analysis of the analysis operator,” J. Funct. Anal., 148, 408–447 (1997).
A. Petukhov, “Explicit construction of framelets,” Appl. Comput. Harmon. Anal., 11, 313–327 (2001).
I. Ya. Novikov, V. Yu. Protasov, and M. A. Skopina, Wavelet Theory, Translations of Mathematical Monographs, 239, AMS, Providence (2011).
G. V. Milovanovic, D. S. Mitrinovic, and Th. M. Rassias, Topics in Polynomials: Extremal Problems, Inequalities, Zeros, World Scientific, Singapure (1994).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 499, 2021, pp. 53–66.
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Lebedeva, E.A., Shcherbakov, I.A. On Refinement Masks of Tight Wavelet Frames. J Math Sci 273, 476–484 (2023). https://doi.org/10.1007/s10958-023-06514-x
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DOI: https://doi.org/10.1007/s10958-023-06514-x