A Characterization of Nonuniform Multiwavelets Using Dimension Function
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In this article, we present a characterization of nonuniform multiwavelets associated to a nonuniform multiresolution analysis (NUMRA) having finite multiplicity in terms of its dimension function. This, in turn, improves the main result of Gabardo and Yu given in (J Math Anal Appl 323(2):798–817, 2006). The concept of NUMRA was introduced by Gabardo and Nashed in which the translation set is a spectrum that is no longer a group.
KeywordsMRA with multiplicity D NUMRA spectral pairs multiwavelets multiscaling functions dimension function
Mathematics Subject Classification42C40 65T60
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- 2.Calogero, A., Garrigós, G.: A characterization of wavelet families arising from biorthogonal MRA’s of multiplicity \(d\). J. Geom. Anal. 11(2), 187–217 (2001)Google Scholar
- 4.Gabardo, J.-P., Nashed, M.Z.: An analogue of Cohen’s condition for nonuniform multiresolution analyses, wavelets, multiwavelets, and their applications (San Diego, CA, 1997), pp. 41–61. Contemp. Math. 216, Amer. Math. Soc., Providence (1998)Google Scholar
- 8.Mittal, S., Shukla, N.K.: Generalized nonuniform multiresolution analyses. Colloq. Math. (to be appear)Google Scholar
- 9.Mittal, S., Shukla, N.K., Atuloba, N.A.S.: Nonuniform multiresolution analyses with finite multiplicity (preprint)Google Scholar
- 12.Wang, X.: The study of wavelets from the properties of their Fourier transforms. Thesis (Ph.D.)-Washington University in St. Louis (1995)Google Scholar
- 13.Yu, X.: Wavelet sets, integral self-affine tiles and nonuniform multiresolution analyses. Thesis (Ph.D.)–McMaster University (Canada) (2005)Google Scholar