Characterization of the closedness of the sum of two shift-invariant spaces

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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 L-2(R-d) 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. (c) 2005 Elsevier Inc. All rights reserved.
Publisher
Academic Press Inc Elsevier Science
Issue Date
2006-08
Language
English
Article Type
Article
Keywords

BIORTHOGONAL WAVELETS; MULTIRESOLUTION ANALYSES; OBLIQUE PROJECTIONS; HILBERT-SPACES; RIESZ BASES; FRAMES; L(2)(R(D)); L-2(R-D)

Citation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.320, no.1, pp.381 - 395

ISSN
0022-247X
DOI
10.1016/j.jmaa.2005.06.097
URI
http://hdl.handle.net/10203/86562
Appears in Collection
MA-Journal Papers(저널논문)
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