Extension of shift-invariant systems in L2(ℝ) to frames

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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In this article, we show that any shift-invariant Bessel sequence with an at most countable number of generators can be extended to a tight frame for its closed linear span by adding another shift-invariant system with at most the same number of generators. We show that in general this result is optimal, by providing examples where it is impossible to obtain a tight frame by adding a smaller number of generators. An alternative construction (which avoids the technical complication of extracting the square root of a positive operator) yields an extension of the given Bessel sequence to a pair of dual frame sequences. © 2012 Taylor and Francis Group, LLC.
Original languageEnglish
JournalNumerical Functional Analysis and Optimization
Publication date2012
Volume33
Journal number7-9
Pages833-846
ISSN0163-0563
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 0

Keywords

  • Functional analysis, Mathematical techniques, Invariance
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