Wavelets in wandering subspaces

Goodman, T. N. T.; Lee, S. L.; Tang, W. S.

doi:10.1090/S0002-9947-1993-1117215-0

Wavelets in wandering subspaces
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by T. N. T. Goodman, S. L. Lee and W. S. Tang PDF

Trans. Amer. Math. Soc. 338 (1993), 639-654 Request permission

Abstract:

Mallat’s construction, via a multiresolution approximation, of orthonormal wavelets generated by a single function is extended to wavelets generated by a finite set of functions. The connection between multiresolution approximation and the concept of wandering subspaces of unitary operators in Hilbert space is exploited in the general setting. An example of multiresolution approximation generated by cardinal Hermite $B$-splines is constructed.

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