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• W2030651946 abstract "We first present a formula for the supremum cosine angle between two closed subspaces of a separable Hilbert space under the assumption that the ‘generators’ form frames for the subspaces. We then characterize the conditions that the sum of two, not necessarily finitely generated, shift-invariant subspaces of L2(Rd) be closed. If the fibers of the generating sets of the shift-invariant subspaces form frames for the fiber spaces a.e., which is satisfied if the shift-invariant subspaces are finitely generated or if the shifts of the generating sets form frames for the respective subspaces, then the characterization is given in terms of the norms of possibly infinite matrices. In particular, if the shift-invariant subspaces are finitely generated, then the characterization is given wholly in terms of the norms of finite matrices." @default.
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• W2030651946 date "2006-08-01" @default.
• W2030651946 modified "2023-09-27" @default.
• W2030651946 title "Characterization of the closedness of the sum of two shift-invariant spaces" @default.
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• W2030651946 doi "https://doi.org/10.1016/j.jmaa.2005.06.097" @default.
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