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arXiv · 1605.02456

On the structure of finitely generated shift-invariant subspaces

K. S. Kazarian
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Abstract

A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an element of the finitely generated shift-invariant subspace as a linear combination of Fourier transformations of generators. An estimate for the norms of those coefficients is derived. For the proof a sort of orthogonalization procedure for generators is used which reminds the well known Gram-Schmidt orthogonalization process.

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K. S. Kazarian. 2016-05-09. On the structure of finitely generated shift-invariant subspaces. https://arxiv.org/abs/1605.02456

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