A characterization of wavelet families arising frombiorthogonal MRA ' s of multiplicity dby
نویسنده
چکیده
In this paper we give a necessary and suucient condition for a pair of wavelet (R n), to arise from a pair of biorthogonal MRA's. The condition is given in terms of simple equations involving the functionsànd ~ `. To work in greater generality, we allow mul-tiresolution analyses of arbitrary multiplicity, based on lattice translations and matrix dilations. Our result extends the characterization theorem of G. Gripen-berg and X. Wang for dyadic orthonormal wavelets in L 2 (R), and includes, as particular cases, the suucient conditions of P. Auscher and P.G. Lemari e in the biorthogonal situation.
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