Publication: Research - peer-review › Journal article – Annual report year: 2012
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.
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- Functional analysis, Mathematical techniques, Invariance