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Wavelets in wandering subspaces. (English) Zbl 0777.41011

Summary: 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.

MSC:

41A15 Spline approximation
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
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