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On the stability of arbitrary biorthogonal wavelet packets. (English) Zbl 0792.42020
If $$\phi$$ and $$\psi$$ generate an orthonormal multiresolution analysis and an orthonormal basis of $$L^ 2= L^ 2(-\infty,\infty)$$, respectively, then various orthonormal bases of $$L^ 2$$ can be easily derived by considering the so-called wavelet packets corresponding to $$\phi$$ and $$\psi$$. In this paper, it is shown that if the same procedure is applied to biorthogonal scaling functions and wavelets, however, not all the resulting wavelet packets lead to Riesz bases of $$L^ 2$$.

##### MSC:
 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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