A frame multiresolution (FMRA for short) orthogonal wavelet is a single-function orthogonal wavelet such that the associated scaling space V 0 admits a normalized tight frame (under translations). In this article, we prove that for any expansive matrix A with integer entries, there exist A-dilation FMRA orthogonal wavelets. FMRA orthogonal wavelets for some other expansive matrix with non integer entries are also discussed.
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Dai, X., Diao, Y., Gu, Q. et al. Wavelets with Frame Multiresolution Analysis. J. Fourier Anal. Appl. 9, 39–48 (2003). https://doi.org/10.1007/s00041-003-0001-5
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DOI: https://doi.org/10.1007/s00041-003-0001-5