an:00447197
Zbl 0792.42020
Cohen, A.; Daubechies, I.
On the stability of arbitrary biorthogonal wavelet packets
EN
SIAM J. Math. Anal. 24, No. 5, 1340-1354 (1993).
00015747
1993
j
42C40 46E30
orthonormal multiresolution analysis; orthonormal bases; wavelet packets; biorthogonal scaling functions; Riesz bases
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 \(L^ 2\).
C.K.Chui (College Station)