Generalized shift invariant systems

@inproceedings{Ron2005GeneralizedSI,
  title={Generalized shift invariant systems},
  author={Amos Ron and Zuowei Shen},
  year={2005}
}
A countable collection X of functions in L2(IR ) is said to be a Bessel system if the associated analysis operator T ∗ X : L2(IR ) → `2(X) : f 7→ (〈f, x〉)x∈X is well-defined and bounded. A Bessel system is a fundamental frame if T ∗ X is injective and its range is closed. This paper considers the above two properties for a generalized shift-invariant system X. By definition, such a system has the form X = ∪j∈JYj , where each Yj is a shift-invariant system (i.e., is comprised of lattice… CONTINUE READING
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