Abstract
We use the matrix-valued Fejér–Riesz lemma for Laurent polynomials to characterize when a univariate shift-invariant space has a local orthonormal shift-invariant basis, and we apply the above characterization to study local dual frame generators, local orthonormal bases of wavelet spaces, and MRA-based affine frames. Also we provide a proof of the matrix-valued Fejér–Riesz lemma for Laurent polynomials.
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Hardin, D.P., Hogan, T.A. & Sun, Q. The Matrix-Valued Riesz Lemma and Local Orthonormal Bases in Shift-Invariant Spaces. Advances in Computational Mathematics 20, 367–384 (2004). https://doi.org/10.1023/A:1027389826705
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DOI: https://doi.org/10.1023/A:1027389826705