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The Structure of Shift-Invariant Subspaces of L2(Rn)

โœ Scribed by Marcin Bownik

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
207 KB
Volume
177
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

Using the range function approach to shift invariant spaces in L 2 (R n ) we give a simple characterization of frames and Riesz families generated by shifts of a countable set of generators in terms of their behavior on subspaces of l 2 (Z n ). This in turn gives a simplified approach to the analysis of frames and Riesz families done by Gramians and dual Gramians. We prove a decomposition of a shift invariant space into the orthogonal sum of spaces each of which is generated by a quasi orthogonal generator. As an application of this fact we characterize shift preserving operators in terms of range operators and prove some facts about the dimension function.

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