Quasi-orthogonal decompositions of structured frames

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Abstract

A decomposition of a Hilbert space Hscr; into a quasi-orthogonal family of closed subspaces is introduced. We shall investigate conditions in order to derive bounded families of corresponding quasi-projectors or resolutions of the identity operator. Given a local family of atoms, or generalized stable basis, for each subspace, we show that the union of the local atoms can generate a global frame for the Hilbert space. Corresponding duals can be calculated in a flexible way by means of systems of quasi-projectors. An application to Gabor frames is presented as example of the use of this technique, for calculation of duals and explicit estimates of lattice constants.

Original languageEnglish
Pages (from-to)180-199
Number of pages20
JournalJournal of Mathematical Analysis and Applications
Volume289
Issue number1
DOIs
StatePublished - 1 Jan 2004
Externally publishedYes

Keywords

  • Decomposition methods
  • Frames
  • Gabor analysis
  • Iterative algorithms
  • Wiener amalgams

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