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Explicitly given pairs of dual frames with compactly supported generators and applications to irregular B-splines. (English) Zbl 1208.41003

Summary: We consider systems of functions appearing by letting a class of modulations act on a countable collection of functions. These systems correspond to shift-invariant systems, considered on the Fourier side. We provide sufficient conditions for the system to be a frame, as well as an explicit construction of a class of frames and associated duals. We use the result to construct frames based on B-splines with knot sequences satisfying a natural condition, as well as explicitly given duals.

MSC:

41A15 Spline approximation
42C15 General harmonic expansions, frames
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